{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting FFT Comparison Experiment...\n",
      "Signal Length N = 1024\n",
      "------------------------------------------------------------\n",
      "K=  1 | Trad: 0.016215s | GMT: 0.028967s | Speedup: 0.56x | Error: 0.00e+00\n",
      "K=  2 | Trad: 0.019903s | GMT: 0.006982s | Speedup: 2.85x | Error: 0.00e+00\n",
      "K=  4 | Trad: 0.016991s | GMT: 0.006984s | Speedup: 2.43x | Error: 0.00e+00\n",
      "K=  8 | Trad: 0.018106s | GMT: 0.007989s | Speedup: 2.27x | Error: 0.00e+00\n",
      "K= 16 | Trad: 0.028668s | GMT: 0.008722s | Speedup: 3.29x | Error: 0.00e+00\n",
      "K= 32 | Trad: 0.017161s | GMT: 0.012966s | Speedup: 1.32x | Error: 0.00e+00\n",
      "K= 64 | Trad: 0.018002s | GMT: 0.008568s | Speedup: 2.10x | Error: 0.00e+00\n",
      "K=128 | Trad: 0.013952s | GMT: 0.010971s | Speedup: 1.27x | Error: 0.00e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "Max Error across all tests: 0.00e+00\n",
      "Peak Speedup: 3.29x\n",
      "Figure saved as 'fft_comparison_results.png'\n",
      "Experiment completed.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "from functools import lru_cache\n",
    "import math\n",
    "\n",
    "# === 1. GMT-FFT 核心实现（带稀疏路径剪枝）===\n",
    "@lru_cache(maxsize=1024)\n",
    "def get_twiddle_cached(N, stage, m, W_step):\n",
    "    \"\"\"\n",
    "    带缓存的旋转因子计算\n",
    "    参数：N: 总长度, stage: 当前层, m: 块内索引, W_step: 步长\n",
    "    \"\"\"\n",
    "    k = m * W_step\n",
    "    return np.exp(-2j * np.pi * k / N)\n",
    "\n",
    "def gmt_fft_sparse(x, threshold=1e-10):\n",
    "    \"\"\"\n",
    "    GMT-FFT：基于生成映射的稀疏路径剪枝版本\n",
    "    输入: x - 实数或复数列表，长度为2的幂\n",
    "    输出: X - DFT结果，仅计算活跃路径\n",
    "    \"\"\"\n",
    "    N = len(x)\n",
    "    X = np.array(x, dtype=complex)  # 转为复数数组\n",
    "    \n",
    "    if (N & (N-1)) != 0:\n",
    "        raise ValueError(\"N must be a power of 2\")\n",
    "    \n",
    "    M = N.bit_length() - 1  # log2(N)\n",
    "    \n",
    "    # --- 位逆序置换 + 初始化活跃索引 ---\n",
    "    active_indices = set()\n",
    "    \n",
    "    for i in range(N):\n",
    "        j = int(f\"{i:0{M}b}\"[::-1], 2)\n",
    "        if j > i:\n",
    "            X[i], X[j] = X[j], X[i]\n",
    "        if abs(X[i]) > threshold:\n",
    "            active_indices.add(i)\n",
    "    \n",
    "    # --- 按层进行蝶形运算（带剪枝）---\n",
    "    for stage in range(M):\n",
    "        span = 1 << stage\n",
    "        W_step = N // (1 << (stage + 1))\n",
    "        active_next = set()\n",
    "        \n",
    "        for k in range(0, N, 1 << (stage + 1)):\n",
    "            for m in range(span):\n",
    "                i1 = k + m\n",
    "                i2 = i1 + span\n",
    "                \n",
    "                # ✅ 剪枝：若两个输入都不活跃，则跳过\n",
    "                if i1 not in active_indices and i2 not in active_indices:\n",
    "                    continue\n",
    "                \n",
    "                active_next.add(i1)\n",
    "                active_next.add(i2)\n",
    "                \n",
    "                W = get_twiddle_cached(N, stage, m, W_step)\n",
    "                t = W * X[i2]\n",
    "                u = X[i1]\n",
    "                X[i1] = u + t\n",
    "                X[i2] = u - t\n",
    "        \n",
    "        active_indices = active_next\n",
    "    \n",
    "    return X\n",
    "\n",
    "# === 2. 传统FFT（用于对比）===\n",
    "def traditional_fft(x):\n",
    "    \"\"\"\n",
    "    传统迭代FFT，无任何剪枝\n",
    "    用于与GMT-FFT进行公平对比\n",
    "    \"\"\"\n",
    "    N = len(x)\n",
    "    X = np.array(x, dtype=complex)\n",
    "    \n",
    "    if (N & (N-1)) != 0:\n",
    "        raise ValueError(\"N must be a power of 2\")\n",
    "    \n",
    "    M = N.bit_length() - 1\n",
    "    \n",
    "    # 位逆序置换\n",
    "    for i in range(N):\n",
    "        j = int(f\"{i:0{M}b}\"[::-1], 2)\n",
    "        if j > i:\n",
    "            X[i], X[j] = X[j], X[i]\n",
    "    \n",
    "    # 所有层全部计算，无剪枝\n",
    "    for stage in range(M):\n",
    "        span = 1 << stage\n",
    "        W_step = N // (1 << (stage + 1))\n",
    "        \n",
    "        for k in range(0, N, 1 << (stage + 1)):\n",
    "            for m in range(span):\n",
    "                i1 = k + m\n",
    "                i2 = i1 + span\n",
    "                W = np.exp(-2j * np.pi * m * W_step / N)\n",
    "                t = W * X[i2]\n",
    "                u = X[i1]\n",
    "                X[i1] = u + t\n",
    "                X[i2] = u - t\n",
    "    \n",
    "    return X\n",
    "\n",
    "# === 3. 实验主函数 ===\n",
    "def run_comparison():\n",
    "    \"\"\"\n",
    "    对不同稀疏度K进行对比实验\n",
    "    测试信号长度 N=1024\n",
    "    K = [1, 2, 4, 8, 16, 32, 64, 128]\n",
    "    \"\"\"\n",
    "    N = 1024\n",
    "    K_list = [1, 2, 4, 8, 16, 32, 64, 128]\n",
    "    \n",
    "    # 存储结果\n",
    "    times_gmt = []\n",
    "    times_trad = []\n",
    "    errors = []\n",
    "    speedups = []\n",
    "    \n",
    "    print(\"Starting FFT Comparison Experiment...\")\n",
    "    print(f\"Signal Length N = {N}\")\n",
    "    print(\"-\" * 60)\n",
    "    \n",
    "    for K in K_list:\n",
    "        # 生成稀疏信号：K个随机位置为1，其余为0\n",
    "        x = np.zeros(N)\n",
    "        indices = np.random.choice(N, size=K, replace=False)\n",
    "        x[indices] = 1.0\n",
    "        \n",
    "        # === 测试传统FFT ===\n",
    "        start = time.time()\n",
    "        X_trad = traditional_fft(x)\n",
    "        t_trad = time.time() - start\n",
    "        \n",
    "        # === 测试GMT-FFT ===\n",
    "        start = time.time()\n",
    "        X_gmt = gmt_fft_sparse(x)\n",
    "        t_gmt = time.time() - start\n",
    "        \n",
    "        # 计算误差（最大绝对误差）\n",
    "        error = np.max(np.abs(X_trad - X_gmt))\n",
    "        \n",
    "        # 记录结果\n",
    "        times_trad.append(t_trad)\n",
    "        times_gmt.append(t_gmt)\n",
    "        errors.append(error)\n",
    "        speedups.append(t_trad / t_gmt if t_gmt > 0 else np.inf)\n",
    "        \n",
    "        print(f\"K={K:3d} | Trad: {t_trad:.6f}s | GMT: {t_gmt:.6f}s | \"\n",
    "              f\"Speedup: {t_trad/t_gmt:4.2f}x | Error: {error:.2e}\")\n",
    "    \n",
    "    # === 绘图 ===\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "    \n",
    "    # 时间对比图\n",
    "    ax1.plot(K_list, times_trad, 's-', label='Traditional FFT', color='red')\n",
    "    ax1.plot(K_list, times_gmt, 'o-', label='GMT-FFT (Pruned)', color='blue')\n",
    "    ax1.set_xlabel('Sparsity K (Number of Non-zeros)')\n",
    "    ax1.set_ylabel('Execution Time (seconds)')\n",
    "    ax1.set_title('Execution Time vs Sparsity')\n",
    "    ax1.set_xscale('log')\n",
    "    ax1.set_yscale('log')\n",
    "    ax1.legend()\n",
    "    ax1.grid(True, alpha=0.3)\n",
    "    \n",
    "    # 加速比图\n",
    "    ax2.plot(K_list, speedups, 'd-', color='green')\n",
    "    ax2.set_xlabel('Sparsity K (Number of Non-zeros)')\n",
    "    ax2.set_ylabel('Speedup (Traditional / GMT)')\n",
    "    ax2.set_title('Speedup of GMT-FFT over Traditional FFT')\n",
    "    ax2.set_xscale('log')\n",
    "    ax2.axhline(y=1.0, color='gray', linestyle='--', alpha=0.7)\n",
    "    ax2.grid(True, alpha=0.3)\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.savefig('fft_comparison_results.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "    \n",
    "    # 输出最终统计\n",
    "    print(\"-\" * 60)\n",
    "    print(f\"Max Error across all tests: {max(errors):.2e}\")\n",
    "    print(f\"Peak Speedup: {max(speedups):.2f}x\")\n",
    "    print(\"Figure saved as 'fft_comparison_results.png'\")\n",
    "    print(\"Experiment completed.\")\n",
    "\n",
    "# === 4. 运行实验 ===\n",
    "if __name__ == \"__main__\":\n",
    "    run_comparison()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实验结果基本上符合预期，加上执行过程可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting FFT Comparison Experiment...\n",
      "Signal Length N = 1024\n",
      "------------------------------------------------------------\n",
      "K=  1 | Trad: 0.016350s | GMT: 0.009563s | Speedup: 1.71x | Error: 0.00e+00\n",
      "K=  2 | Trad: 0.019936s | GMT: 0.007519s | Speedup: 2.65x | Error: 0.00e+00\n",
      "K=  4 | Trad: 0.018879s | GMT: 0.008702s | Speedup: 2.17x | Error: 0.00e+00\n",
      "K=  8 | Trad: 0.018488s | GMT: 0.007852s | Speedup: 2.35x | Error: 0.00e+00\n",
      "K= 16 | Trad: 0.015468s | GMT: 0.008622s | Speedup: 1.79x | Error: 0.00e+00\n",
      "K= 32 | Trad: 0.014969s | GMT: 0.007565s | Speedup: 1.98x | Error: 0.00e+00\n",
      "K= 64 | Trad: 0.014213s | GMT: 0.009939s | Speedup: 1.43x | Error: 0.00e+00\n",
      "K=128 | Trad: 0.015738s | GMT: 0.007626s | Speedup: 2.06x | Error: 0.00e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "Max Error across all tests: 0.00e+00\n",
      "Peak Speedup: 2.65x\n",
      "Figure saved as 'fft_comparison_results.png'\n"
     ]
    },
    {
     "data": {
      "image/png": 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ukjnAh4FPAu9qv5+18QTgl9OMUZKkaTGhlKSZ61u07occU1XdB3wQ+Pdm18nAe0emhSbZMMlBzbGvAAckeVqS2bQWzBn3d0jzyI45473GOqdJ9B4HPAXYuXk9kdY9hodU1Y20Ft/5WJL1kqyS5BnN6X8AHpVknWV8Ho9tYj+jqkam7J4NbNssOrRK89otyRMmqGuZquoB4Ku0ksE1mvs22xcZWla7HwEuah598k1a16fd3rQ+D0mSVhgTSkmauT4DPDvJ6hOUOQ3YIsmBtBKYbwDnJrkd+DmwO0BVLQJeSyu5u5HWdNrFY9Y4dYcA/1NVv6qq34+8mrgOaEboXkrrnsXLgJuAI5v4LqM1Anl1M330Ec+vbEZlvwr8ddOPkf23A/vSmgZ7A/B74D+AVbvQp9fRmv76e+B0WovrLLPdJpHfDziiKf6vwK5JXgKQZDfgzubxIZIkrTCp6mSWkCRpECV5H3BTVX14Rcei7kny38Anm0WAJElaYUwoJUmSJElT4pRXSZIkSRoQSU5LclOSX49zPEmOT3JVkktGPc+560woJUmSJGlwnE7rPvvx7A9s07wOB07qZTAmlJIkSZI0IKrqh8AtExQ5CPhMtfwcWDfJxr2KZ+VeVTwompUND1x99dUP23yzzTo+7/6l97PKyqv0pPyg1t1Psfx5yc3U/UuXXbCxxobrD2Q/B7XuforFfs6sWAa17n6KZbJ1T+b7dp2NN7KfXYilX+rup1gGte5+iqWf+nnFlVcuqaoNO668j2yeleuejh6NPL4lPLgIuKdt16lVdeokqtiU1rOORyxu9t04rcDGMfQJZVWdBZy13bbbHnb5wgs6Pm/+T37GPnvt0ZPyg1p3P8Xy5r87mDvm/7Tjul/01ZMGsp+DWnc/xWI/Z1Ysg1p3P8Uy2bon83178sIL7GcXYumXuvsplkGtu59i6ad+Zs11r+u44j5zD8XzWHNadZzC7fdU1dxpVJEx9vVsJdahTyglSZIkqRtCX9xTuBjYvG17M1rPO+6JPuivJEmSJKlLvgG8rFnt9anAbVXVk+mu4AilJEmSJHXNrIw143QSljE5NckXgX2ADZIsBt4JrAJQVScD3wKeDVwF3AW8fHoBTcyEUpIkSZK6YHlMea2qFy/jeAGv7XEYf2FCKUmSJEldMmuaA5S9Wz6nN7yHUpIkSZI0JY5QSpIkSVKXDNuInQmlJEmSJHVByPQX5RkwJpSSJEmS1CXDNkI5bP2VJEmSJHWJI5SSJEmS1AWhC6u8DhgTSkmSJEnqkmGbAjps/ZUkSZIkdYkjlJIkSZLUDYG4yqskSZIkabLC8E0BNaGUJEmSpC4ZtkV5hi2BliRJkiR1iSOUkiRJktQlwzZiZ0IpSZIkSV3Qeg7lcM15HbYEeqh9/FOrMG/f/fjXt64GwH33wfa7zGGNDdbmmmtD1lznYa8j/221FRyxhtHHP7UKWXOdh/2cvuwVT2ONDdbmIyfOZtc957DWRmuzwRZr8YojVufuux8695RPzmazbdbibw/4Gw46eA1uvnm4vtAldcdY30On/eITfJI/8GceC8CtbMvHWcIp3M7VHATA7WzBKdxO1lyHefvu5+9SaUjNmuZr0PQs5iRHJ1mU5JIkC5Ps3uw/MskavWq3rf1DklzZvA7pdXuD4FWH3s+OO9zK8SfNZuEvZ/GBD67K5VesxDveei8j/5ByxKvu5Yun38UXT7+LQ15y34oNWEPpVYfez55PXfqwn9PrF8/hHW+9lz/fHnbY/gE+9IG7efLOD/Cpz87mP49bFYAFC2dxxBtW5wnbPcChL7uKb35nZd74Vv8iJ2nyxvoeuvXuzdmFY1mb6yjgh5zALJaOef4Rr7qX/+9tC/1dKmko9GTKa5I9gAOAXavq3iQbALObw0cCnwPu6kXbTfvrA+8E5gIFXJTkG1V1a6/aHAQJ/Ou/LOLVr92Ll75qDa66ehZP2P4B/u3Ie/ndDa2Mcu6uD/Ccv7ufNZqUf/5PVmDAGkoJnPyRu9l1rzl/+Tl97BZ38G9HPkAVzG6+SZ662wPstPsqLLq09e9ip3+udeB9x9zLnfdcw6WXPo4vfnkVTv3o3axmXilpEsb6Hlp/jet40l0fBuA3vIrb2YIn8Cl+xesecf7cXR9g081uYr9nbbWcI5e0orWmvK7oKJavXo1Qbgwsqap7AapqSVXdkOQNwCbAeUnOA0hyUpILm9HMY0YqSPLsJJcl+XGS45Oc3exfM8lpSS5IsiDJQWO0/7fAd6vqliaJ/C6wX4/6OlC23uoOjnztffz6Nytxzz3hpA/fzSqrPHT8sNeuzpobrsOOc+fw8/NXWnGBaqj91RMffNjP6ZFvWMQqqzyUTAKc87+tfw97xl4PAHDNda2vs003eRCAzTZ5kKVLw/WLB3HyiKQVbfT30F9vewIrsZQ72ZjzeRdP543M5s9jnnvYa1dn/+fs6+9SaUg55bU7zgU2T3JFko8l2Rugqo4HbgDmVdW8puzRVTUX2AnYO8lOSVYDTgH2r6qnARu21X008P2q2g2YBxybZM1R7W8KXN+2vbjZ9zBJDm+S2Qtvu+22aXd6UNz4+4f+2eT3f2j9CKy5Bhzzjnv4+hl38V/vu5srrpzFS16x+ooKUXrYz+ktt6z6sGP//fWVefu7VuPZf3s//3zY2NPJqlp/Dtl98ZK6qP176M771gfgFxzDBixgXa7gXtYD4C424n7WZGXuYi7/j6+fcRf/fPhl/i6VhtQsMq3XoOlJQllVdwBPBg4H/gickeTQcYofnORiYAGwI7ADsD1wdVVd05T5Ylv5fYGjkiwE5gOrAVuMqnOsK1FjxHlqVc2tqrnrrLNOBz0bfBctWJ/PnzGbZ+2zlPXXf5Aj37Iat90GG25Y/Pvb7uU5f7eUN/3Lfez0xAe5+pqVuO++Qfx3Eg2675230sN+Tk88eXtG/s3njK+swosOWYN5z1jKf3/hLlZq/vF/q8e2RiYX/671M/u7G2ex8srFZps+uCK6IGnAjf4emn/Vq7mXtbmDzbiBffgSv+TX/DMAP+GDXMMBrM4Snsx/8Jy/W8rBz7/2L79L77lnBXdGknqoZ48NqaoHaCV885P8CjgEOL29TJKtgDcDu1XVrUlOp5UgTpSaB3heVV0+QZnFwD5t25s1sQy1e++FDx+/I2usUXzypLv43/NW5lWvWYO3v2s1dt7pAS64aGV2320p11w7i4WXzOJJf/UAs2f7l3EtX/feC/985Opj/JyGZ//tUl7yitVZb73ixS+4n6+ftQqP3vBBnrnPA7zsJfdx/EmrcvS7VmXrx23FT3++Ei9+wf3ePylp0sb+HnoU5/NO5vJe7mEDAP6Pf+Bq/oGdOJ6N+QmXcig3sSuf/PQqzP/RNn/5Xer3kDQ8vIeyS5Jsl2Sbtl07A9c1728H1mrerw3cCdyWZCNg/2b/ZcDWSbZstl/YVtc5wOuT1kS2JLuMEcI5wL5J1kuyHq1RzXOm1akZ4H3Hrsri363JO992D4/donjFy+7n6Xst5eRPzGbbxz/IJb+exZFvWZ0TT12V/f5mKV/+XM/WTZLG9b5jV+XKq1Z62M/pTk+8hZM/MZsTT5nNAw+EJUtm8fIj1uDFh67Buz/Q+pvak3d5kBOPu5vfXLYSn/r049l/36Uc9x8OC0iavLG+hzZd51dcyitZmXvYmv9ha/6H9bgMgI04n7VYzDpcyS08kSPfsjpfP2sLf5dKQ2rY7qHs1QjlHOCEJOsCS4GraE1/BTgV+HaSG6tqXpIFwCLgauAnAFV1d5LXAN9JsgQ4v63u9wAfBi5pkspraa0o+xdVdUuS9wAXNLveXVW3dL2XA+aYd9zLvHnz2WevPYDWvWU/PPfOvxz/+fw7H3HO7/6w3MKTgNbP6THvuPcv2wl85EPn/+XndiKvOfw+XnP4fcz/yc86Ki9JYxnre+hFu7yZO+b/9GHl5vJ+5vL+v2xvwk/4e57JyX9Y7PeQNKSS4Ruh7ElCWVUXAXuOc+wE4IS27UPHqea8qtq+SRpPBC5syt8NvLqDGE4DTptc5JIkSZKkTvXsHsouOCzJIbSeX7mA1qqvkiRJktS3BnGl1uno24Syqo4DjlvRcUiSJElSp4Ztyusg3vcpSZIkSeoDfTtCKUmSJEmDJAzfiJ0JpSRJkiR1ybBNeTWhlCRJkqQuCBm6RXmGbURWkiRJktQljlBKkiRJUpc45VWSJEmSNCVDlk+aUEqSJElSN4ThG6H0HkpJkiRJ0pQ4QilJkiRJXTJsq7yaUEqSJElSFyTDN+XVhFKSJEmSumTY7ikctv5KkiRJkrrEEUpJkiRJ6pIhm/FqQilJkiRJ3dB6bMhwpZROeZUkSZIkTYkjlJIkSZLUJcM1PgmpqhUdwwqV5EDgwI02evRhX/rspzs+79rfLmbLLTbrSflBrbufYjn3C1/hvmuv77ju2Vtu3nH5A97+xr7p56DW3U+x2M+ZFcug1t1PsUy27l5+3z7xn17g74lplvfntr/r7qdY+qmf8/bd/6Kqmttx5X3kcSuvUh9Ya/1p1XHwn24aqP4P/QhlVZ0FnLXdttsets9ee3R83nx+Rq/KD2rd/RTL2e87jjvm/7Tjuufss2fH5ff55pl9089BrbufYrGfMyuWQa27n2KZbN29/L7d8u1v9PfENMv7c9vfdfdTLP3Uz0E3bCOU3kMpSZIkSZqSoR+hlCRJkqRuyZCt8mpCKUmSJEldEIZvyqsJpSRJkiR1ybDdUzhs/ZUkSZIkdYkjlJIkSZLUJUN2C6UJpSRJkiR1S4bsLkoTSkmSJEnqgmFclMd7KCVJkiRJU+IIpSRJkiR1ybCNUJpQSpIkSVKXzBqyjNIpr5IkSZKkKXGEUpIkSZK6Iq7yKkmSJEmavGFc5dWEUpIkSZK6IZAhyyi9h1KSJEmSBkiS/ZJcnuSqJEeNcXydJGcl+WWSRUle3qtYTCglSZIkqUsyzdcy609WAk4E9gd2AF6cZIdRxV4L/KaqngTsA3wwyexpdWwcTnmVJEmSpC6Z1fu7KJ8CXFVVVwMk+RJwEPCbtjIFrJUkwBzgFmBpL4IxoZQkSZKkLujSojwbJLmwbfvUqjq1bXtT4Pq27cXA7qPq+CjwDeAGYC3ghVX14PRDeyQTSkmSJEnqH0uqau4Ex8fKWWvU9t8CC4FnAo8DvpvkR1X15+6E+JCe3UOZ5OjmBtBLkixMsnuz/8gka/Sq3bb2v5PkT0nO7nVbkiRJkgStVV6n8+rAYmDztu3NaI1Etns58NVquQq4Bti+G/0brScJZZI9gAOAXatqJ+CveWhY9kig5wklcCzw0uXQjiRJkiQBvV+UB7gA2CbJVs1COy+iNb213W+BZwEk2QjYDrh66r0aX69GKDemNVR7L0BVLamqG5K8AdgEOC/JeQBJTkpyYTOaecxIBUmeneSyJD9OcvzISGOSNZOcluSCJAuSHDRWAFX1PeD2HvVPkiRJkh4h0/xvWapqKfA64BzgUuDMqlqU5IgkRzTF3gPsmeRXwPeAt1bVkl70t1f3UJ4L/HuSK4D/Bc6oqh9U1fFJ/hWY19aho6vqlmb52+8l2Qm4AjgFeEZVXZPki211Hw18v6pekWRd4Pwk/1tVd042yCSHA4cDbPToR0+1r5IkSZK03FTVt4Bvjdp3ctv7G4B9l0csPRmhrKo7gCfTStb+CJyR5NBxih+c5GJgAbAjrWepbA9cXVXXNGXaE8p9gaOSLATmA6sBW0wxzlOram5VzV1nnXWmUoUkSZIkAa0pq7Myvdeg6dkqr1X1AK2Eb34z1HoIcHp7mSRbAW8GdquqW5OcTitBnOijDPC8qrq8B2FLkiRJ0pQNYE44Lb1alGe7JNu07doZuK55fzutZ6EArA3cCdzW3Cy6f7P/MmDrJFs22y9sq+sc4PXNQzpJskvXOyBJkiRJU7AcFuXpK70aoZwDnNDc47gUuIrmXkXgVODbSW6sqnlJFgCLaK069BOAqro7yWuA7yRZApzfVvd7gA8DlzRJ5bW0VpR9mCQ/ojV1dk6SxcArq+qcbndUkiRJkoZVTxLKqroI2HOcYycAJ7RtHzpONedV1fZN0ngicGFT/m7g1R3E8PRJhi1JkiRJ09LJSq0zSa8eG9INhzUL7ywC1qG16qskSZIk9a1keq9B07NFeaarqo4DjlvRcUiSJEmSxta3CaUkSZIkDZLQ31NAe8GEUpIkSZK6ZABnrU6LCaUkSZIkdUkG8UbIaRi2EVlJkiRJUpc4QilJkiRJXTJc45MmlJIkSZLUFcGEUpIkSZI0FYn3UEqSJEmS1AlHKCVJkiSpS2YN1wClCaUkSZIkdUuGLKM0oZQkSZKkLggwZLdQeg+lJEmSJGlqHKGUJEmSpG7I8I1QmlBKkiRJUpf42BBJkiRJkjrgCKUkSZIkdcmQDVCaUEqSJElStwzblNdU1YqOYYVKciBw4EYbPfqwL3320x2fd+1vF7PlFpv1pPyg1j3Z8ud+4Svcd+31Hdc9e8vNOy4/mbKTLX/A29/YN5/5oNbdT7HYz5kVy6DW3U+xTLbuQf0u72XdvYyln34HTba8dfd3LP3Uz3n77n9RVc3tuPI+8sRVV60zN9t0WnXsePU1A9X/oR+hrKqzgLO223bbw/bZa4+Oz5vPz+hV+UGte7Llz37fcdwx/6cd1z1nnz07Lj+ZspMtv883z+ybz3xQ6+6nWOznzIplUOvup1gmW/egfpf3su5extJPv4MmW966+zuWfuqnBsvQJ5SSJEmS1BWBWUM25dWEUpIkSZK6ZMjySRNKSZIkSeqODN2iPD6HUpIkSZI0JY5QSpIkSVIXBMiQDdmZUEqSJElSN2T4nkNpQilJkiRJXTJk+aT3UEqSJEmSpsYRSkmSJEnqEqe8SpIkSZKmZMjySRNKSZIkSeqGALOGLKP0HkpJkiRJ0pQ4QilJkiRJ3RCnvEqSJEmSpmjYFuVxyqskSZIkaUocoZQkSZKkLhmyAUoTSkmSJEnqhmBCKUmSJEmaioTMGq6M0nsoJUmSJElT4gilJEmSJHXJsE157dkIZZKjkyxKckmShUl2b/YfmWSNXrXbtLFzkp+1tf/CXrYnSZIkSQCzkmm9Bk1PRiiT7AEcAOxaVfcm2QCY3Rw+EvgccFcv2m7cBbysqq5MsglwUZJzqupPPWxTkiRJ0hAbxkV5ejVCuTGwpKruBaiqJVV1Q5I3AJsA5yU5DyDJSUkubEYTjxmpIMmzk1yW5MdJjk9ydrN/zSSnJbkgyYIkB41uvKquqKorm/c3ADcBG/aor5IkSZI0lHqVUJ4LbJ7kiiQfS7I3QFUdD9wAzKuqeU3Zo6tqLrATsHeSnZKsBpwC7F9VT+PhyeDRwPerajdgHnBskjXHCyTJU2iNjv7fGMcOb5LZC2+77bZpd1qSJEnScEsyrdeg6UlCWVV3AE8GDgf+CJyR5NBxih+c5GJgAbAjsAOwPXB1VV3TlPliW/l9gaOSLATmA6sBW4xVcZKNgc8CL6+qB8eI89SqmltVc9dZZ51J9VGSJEmSHiatKa/TeQ2anq3yWlUP0Er45if5FXAIcHp7mSRbAW8GdquqW5OcTitBnOijDPC8qrp8ovaTrA18E3hHVf18it2QJEmSpI4N4ijjdPRkhDLJdkm2adu1M3Bd8/52YK3m/drAncBtSTYC9m/2XwZsnWTLZrt9ldZzgNenuVJJdhmj/dnA14DPVNWXp90hSZIkSdIj9GqEcg5wQpJ1gaXAVbSmvwKcCnw7yY1VNS/JAmARcDXwE4CqujvJa4DvJFkCnN9W93uADwOXNEnltbRWlG13MPAM4FFtU20PraqFXeyjJEmSJD3MkA1Q9iahrKqLgD3HOXYCcELb9qHjVHNeVW3fJI0nAhc25e8GXr2M9j9H69EkkiRJkrRctB4bMlwZZa9Wee2Gw5qFdxYB69Ba9VWSJEmS1Cc6HqFMsmZV3dnLYNpV1XHAccurPUmSJEmalkD6eciuB5bZ3SR7JvkNcGmz/aQkH+t5ZJIkSZI0UKb3DMpBnC7bSf58HPC3wM0AVfVLWgveSJIkSZLazcr0XgOmowHZqrp+1K4HehCLJEmSJGmAdHIP5fVJ9gSqeb7jG2imv0qSJEmS2gzgtNXp6GSE8gjgtcCmwGJg52ZbkiRJkjQiLJd7KJPsl+TyJFclOWqcMvskWZhkUZIfdLWfbZY5QllVS4CX9CoASZIkSZoxenwfZJKVgBOBv6E14HdBkm9U1W/ayqwLfAzYr6p+m+TRvYpnmQllkuPH2H0bcGFV/U/3Q5IkSZIkjeMpwFVVdTVAki8BBwG/aSvzj8BXq+q3AFV1U6+C6WTK62q0prle2bx2AtYHXpnkw70KTJIkSZIGS1r3UE7nBRskubDtdfioRjYF2hdNXdzsa7ctsF6S+UkuSvKyXvW4k0V5Hg88s6qWAiQ5CTiX1hDrr3oVmCRJkiQNkgQy/SmvS6pq7kTNjLGvRm2vDDwZeBawOvCzJD+vqiumG9xonSSUmwJr0prmSvN+k6p6IMm93Q5IkiRJkgZW71d5XQxs3ra9GXDDGGWWVNWdwJ1Jfgg8CVghCeV/AguTzKeVDT8DeF+SNYH/7XZAkiRJkqRxXQBsk2Qr4HfAi2jdM9nuf4CPJlkZmA3sDhzXXiDJ+hM1UlW3dBJMJ6u8fjLJt2jd/Bng7VU1kgH/WyeNSJIkSdIw6MKU1wlV1dIkrwPOAVYCTquqRUmOaI6fXFWXJvkOcAnwIPCJqvr1qKouojVVdrwptFt3Ek8nI5QA9wA30lqg5/FJHl9VP+zwXEmSJEkaDr2f8kpVfQv41qh9J4/aPhY4doI6tupGLJ08NuRVwL/Qmpu7EHgq8DPgmd0IQJIkSZK0YiQJ8BJgq6p6T5ItgMdU1fmdnN/JY0P+BdgNuK6q5gG7AH+casCSJEmSNCMlMGuar+XvY8AePHQf5u3AiZ2e3MmU13uq6p4kJFm1qi5Lst0UApUkSZKkGS3LYcprl+1eVbsmWQBQVbcmmd3pyZ0klIuTrAt8Hfhuklt55LK00tA4Ys3NmLPPnnxp/gs6Kj+ZspMtP5myJ9+5uOMYJEmSNEUrZpRxOu5PshLNsyyTbEhrIZ+OpGr0MzAnKJzsDawDfLuq7p9koH0pyYHAgRtt9OjDvvTZT3d83rW/XcyWW2zWk/KDWvdky5/7ha9w37XXd1z37C0377j8ZMr2uny/1H3A2984sD8rg1p3P8ViP/u77n6KZbJ1D+p3+aD+nvC7fGbV3U+x9FM/5+27/0VVNbfjyvvIruvOqR/ts9O06pjzPz9brv1P8hLghcCuwKeB5wPvqKovd3J+J4vyfLaqXgpQVT8Y2Qe8dKpB95OqOgs4a7tttz1sn7326Pi8+fyMXpUf1LonW/7s9x3HHfN/2nHdc/bZs+Pykynb6/L9Uvc+3zxzYH9WBrXuforFfvZ33f0Uy2TrHtTv8kH9PeF3+cyqu59i6ad+DrSwXFZ57aaq+nySi4Bn0erBc6vq0k7P72TK647tG81w6JMnFaUkSZIkDYF0suxpH0nyEeCMqup4IZ5243Y3yduS3A7slOTPzet24Cbgf6YWriRJkiTNYMn0XsvfxcA7klyV5Ngkk5puO25CWVXvr6q1gGOrau3mtVZVPaqq3jbdqCVJkiRJK1ZVfbqqng08BbgC+I8kV3Z6/rhTXpM8FvjTSPKYZB7wXOBa4MSqum8acUuSJEnSzJKQwVvldcTjge2BLYHfdHrSRDN8zwTWBEiyM/Bl4LfAzrQefilJkiRJajdgU16TjIxIvhv4NfDkqjqw0/MnWpRn9aoaed7kPwGnVdUHk8wCFk41YEmSJEmasQZvhPIaYI+qWjKVkycaoWz/JJ4JfA+gqjp+yKUkSZIkqa+dCuyX5N8BkmyR5CmdnjzRCOX3k5wJ3AisB3y/aWBjwPsnJUmSJKlNa9bqwI1Qngg8SGsQ8d3A7cB/A7t1cvJECeWRwAuBjYGnVdX9zf7HAEdPMVhJkiRJmrkGb8rr7lW1a5IFAFV1a5LZnZ48bkJZVQV8aYz9C6YUpiRJkiTNaCvsWZLTcX+SlYACSLIhrRHLjkx0D6UkSZIkaWY7Hvga8Ogk7wV+DLyv05MnmvIqSZIkSZqEQbuHsqo+n+Qi4Fm0FmZ9LnBbp+ebUEqSJElSN4RBvIeSqroMuGxkO8lvgS06OXeZCWWSvYB3AY9tyqfVZm09lWAlSZIkSX2t46y4kxHKTwJvBC4CHphqRJIkSZI00w3alNdxVKcFO0kob6uqb08jGEmSJEkaDgMy5TXJCYydOAZYt9N6Okkoz0tyLPBV4N6RnVV1caeNSJIkSdKMl4F6bMiFUzz2MJ0klLs3f85t21fAMzttRJIkSZLUP6rq092oZ5kJZVXN60ZDkiRJkjTTZUCmvHbLrGUVSLJOkg8lubB5fTDJOh2cd3SSRUkuSbIwye7N/iOTrNGN4Cdo+7FJLmraXZTkiF62J0mSJEnAQ9Nep/oaMJ1MeT0N+DVwcLP9UuBTwD+Md0KSPYADgF2r6t4kGwCzm8NHAp8D7ppizJ24EdizaXsO8Osk36iqG3rYpiRJkqRhNoDPoUyyflXdMtXzlzlCCTyuqt5ZVVc3r2OAZT2DcmNgSVXdC1BVS6rqhiRvADahtdDPeU0HTmpGPhclOWakgiTPTnJZkh8nOT7J2c3+NZOcluSCJAuSHDS68aq6b6RtYNUO+ylJkiRJw+YXSb7c5F+TzoY7SbTuTvK0kY0kewF3L+Occ4HNk1yR5GNJ9gaoquOBG4B5bfdmHl1Vc4GdgL2T7JRkNeAUYP+qehqwYVvdRwPfr6rdgHnAsUnWHB1Aks2TXAJcD/yHo5OSJEmSei3JtF4rwLbAqbRmol6V5H1Jtu305E4Syn8GTkxybZLrgI8CE96TWFV3AE8GDgf+CJyR5NBxih+c5GJgAbAjsAOwPXB1VV3TlPliW/l9gaOSLATmA6sBW4wRw/VVtRPweOCQJBuNLpPk8JF7Q2+77baJuiRJkiRJy5DWlNfpvJazavluVb0YeBVwCHB+kh80tzJOqJNVXhcCT0qydrP95w4De4BWwjc/ya+awE5vL5NkK+DNwG5VdWuS02kliBN9kgGeV1WXdxjHDUkWAU8HvjLq2Km0snG223bbsR7qKUmSJEmdG7CFdZI8CvgnWiOUfwBeD3wD2Bn4MrDVROePm1Am+aeq+lySfx21H4Cq+tAE524HPFhVVza7dgaua97fDqwFLAHWBu4EbmtGEPenlYReBmydZMuquhZ4YVv15wCvT/L6qqoku1TVglHtbwbcXFV3J1kP2AsYN15JkiRJGlI/Az4LPLeqFrftvzDJycs6eaIRypH7Etca49iyRvPmACckWRdYClxFa/ortEYEv53kxqqal2QBsAi4GvgJQJMIvgb4TpIlwPltdb8H+DBwSXPT6LW0VpRt9wTgg0mK1ojmf1XVr5YRsyRJkiRNXRi4EUrgHVV1ZvuOJC+oqi9X1X8s6+RxE8qqOqV5+79V9ZNRDew1UaVVdRGw5zjHTgBOaNs+dJxqzquq7Zuk8UTgwqb83cCrl9H+d2kt8iNJkiRJy8/gJZRHAWeO2vc2WtNdl6mT51CeAOzawb5uOyzJIbSeX7mA1qqvkiRJkqRpSrI/8Gxg0yTHtx1am9Ys045MdA/lHrRGGTccdR/l2sBKkwt38qrqOOC4XrcjSZIkSd0RmNXJgzT6wg20ZoE+B7iobf/twBs7rWSiEcrZtO6FXJmH30f5Z+D5HYcpSZIkScNiQKa8VtUvgV8m+XxVdTwiOdpE91D+APhBktOr6rrxykmSJEmSGKhFeZKcWVUHAwuaxUwfpqo6WpOmk3so70pyLLAjrWdEjjTwzE6DlSRJkiT1lX9p/hz9xIxJ6WSC7+dpPRdyK+AYWo/puGA6jUqSJEnSjJRM77WcVNWNzdt/AJZW1XXtr07r6SShfFRVfRK4v6p+UFWvAJ46hZglSZIkaQZrFuWZzmv5Wxs4N8mPkrw2yUaTObmTiO9v/rwxyd8l2QXYbLJRSpIkSdKMNyAjlCOq6piq2hF4LbAJrXV0/rfT8zu5h/L/JVkHeBOt50+uzSSWkZUkSZIk9b2bgN8DNwOP7vSkCRPKJCsB21TV2cBtwLzpRChJkiRJM9YArfI6Isk/Ay8ENgS+AhxWVb/p9PwJE8qqeiDJc4DjphWlJEmSJA2DAUsogccCR1bVwqmc3MmU158m+ShwBnDnyM6qungqDUqSJEnSzJQVtbDOpCVZu6r+DPxns71++/GquqWTejpJKPds/nx3e/2Az6GUJEmSpMH0BVrPoLyIVn7XPrRawNadVLLMhLKqvG9SkiRJkjoxIFNeq+qA5s+tplPPMsdjk2yU5JNJvt1s75DkldNpVJIkSZJmnJFFeQbosSFJvtfJvvF0MsH3dOAcWs8kAbgCOLLTBiRJkiRJ/SXJas19kxskWS/J+s1rSx7K/Zapk3soN6iqM5O8DaCqliZ5YGphS5IkSdIMNiBTXoFX0xoo3ITWfZQjgf8ZOLHTSjpJKO9M8ihaN2aS5Km0nkkpSZIkSWqEkAFZ5bWqPgJ8JMnrq+qEqdbTSUL5r8A3gMcl+QmtB14+f6oNSpIkSdKMNTgjlCMeTLJuVf0JIMl6wIur6mOdnJyqWnahZGVgO1rDoJdX1f1Tj7e/JDkQOHDdOXMOe+XcPZdZfsTsLTfnvmuv70n5Qa27n2Kxn490wNvfyLW/XcyWW2zWUfnJlO11+UGtu59iGZZ+nvuFr/TF/2+9Lj+odfdTLIPaT7/LZ1bd/RRLP/Vz3r77X1RVczuuvI/M3WSD+sWrD5xWHSu/6/Tl2v8kC6tq51H7FlTVLp2c38kIJcBTgC2b8rsmoao+M5lA+1VVnQWc9Zi11jnsjvk/7fi8OfvsSa/KD2rd/RSL/Xykfb55JvP5GfvstUdH5SdTttflB7XufoplWPp59vuO64v/33pdflDr7qdYBrWffpfPrLr7KZZ+6udAG1nldbDMSpJqRhqTrATM7vTkZSaUST4LPA5YCIwsxlPAjEgoJUmSJKlrBi+hPAc4M8nJtPK8I4DvdHpyJyOUc4EdqpO5sZIkSZI0tAIDsihPm7cChwP/TGuM9Vzg452e3Elvfw08ZkqhSZIkSZL6VlU9WFUnV9Xzq+p5wCKg41VfO3oOJfCbJOcD97Y1/JxJRytJkiRJM9ngTXklyc7Ai4EXAtcAX+303E4SyndNKSpJkiRJGiYDtChPkm2BF9FKJG8GzqD1FJB5k6lnmVNeq+oHwLXAKs37C4CLJxuwJEmSJM14yfReHTWR/ZJcnuSqJEdNUG63JA8kef4Yhy8DngUcWFVPq6oTeGgR1o4tM6FMchjwFeCUZtemwNcn25AkSZIkaXqax3qcCOwP7AC8OMkO45T7D1qruI7lecDvgfOSfDzJs2iNsU5KJ4vyvBbYC/gzQFVdCTx6sg1JkiRJ0szWrPI6ndeyPQW4qqqurqr7gC8BB41R7vXAfwM3jVVJVX2tql4IbA/MB94IbJTkpCT7dtrjTiK+twkUgCQr03o+iSRJkiSp3fSnvG6Q5MK21+GjWtgUuL5te3Gzry2EbAr8PXDyssKtqjur6vNVdQCwGbAQGHca7WidLMrzgyRvB1ZP8jfAa4CzOm1AkiRJkoZCdxblWVJVc5fRymijB/w+DLy1qh7IJOKpqlto3ep4yrLKjugkoTwKeCXwK+DVwLeAT3QclSRJkiSpWxYDm7dtbwbcMKrMXOBLTTK5AfDsJEur6uvdDmaZCWVVPQh8vHlJkiRJksaUTu+DnI4LgG2SbAX8jtajP/6xvUBVbfWXiJLTgbN7kUzCBPdQJjkoyWvbtn+R5Orm9YJeBCNJkiRJA63Hjw2pqqXA62it3nopcGZVLUpyRJIjety7R5hohPIttLLdEasCuwFrAp8CvtzDuCRJkiRJY6iqb9G6FbF935gL8FTVob2MZaKEcnZVta8e9OOquhm4OcmavQxKkiRJkgbS9BflGSgTJZTrtW9U1evaNjfsTTiSJEmSNKC6s8rrQJnojtFfJDls9M4krwbO711IkiRJkjSImkV5pvMaMBONUL4R+HqSfwQubvY9mda9lM/tcVySJEmSpD43bkJZVTcBeyZ5JrBjs/ubVfX95RKZJEmSJA2aIZvy2slzKL8PmERKkiRJ0rIMWULZs0m6SY5OsijJJUkWJtm92X9kkjV61e6oGNZO8rskH10e7UmSJEkaYgEya3qvAbPMEcqpSLIHcACwa1Xdm2QDYHZz+Ejgc8BdvWh7lPcAP1gO7UiSJEnS0OlVCrwxsKSq7gWoqiVVdUOSNwCbAOclOQ8gyUlJLmxGM48ZqSDJs5NcluTHSY5Pcnazf80kpyW5IMmCJAeNFUCSJwMbAef2qI+SJEmS1CYwa5qvAdOrhPJcYPMkVyT5WJK9AarqeOAGYF5VzWvKHl1Vc4GdgL2T7JRkNeAUYP+qehoPf+7l0cD3q2o3YB5wbJI12xtPMgv4IPBvEwWZ5PAmmb3wrvvvm3anJUmSJA25IZvy2pOIq+oOWo8YORz4I3BGkkPHKX5wkouBBbRWk90B2B64uqquacp8sa38vsBRSRYC84HVgC1G1fka4FtVdf0y4jy1quZW1dw1Vpk9UVFJkiRJWrZkeq8B05N7KAGq6gFaCd/8JL8CDgFOby+TZCvgzcBuVXVrktNpJYgTfZIBnldVl09QZg/g6UleA8wBZie5o6qOmmJ3JEmSJEmj9GSEMsl2SbZp27UzcF3z/nZgreb92sCdwG1JNgL2b/ZfBmydZMtm+4VtdZ0DvD5ppe9JdhndflW9pKq2qKotaSWsnzGZlCRJktRTCcyaNb3XgOnVCOUc4IQk6wJLgatoTX8FOBX4dpIbq2pekgXAIuBq4CcAVXV3M7r4nSRLgPPb6n4P8GHgkiapvJbWirKSJEmStGIN4LTV6ehJQllVFwF7jnPsBOCEtu1Dx6nmvKravkkaTwQubMrfDbx6ErGczqiptpIkSZKk6evZPZRdcFiSQ2g9v3IBrVVfJUmSJKl/DeBKrdPRtwllVR0HHLei45AkSZKkjjnlVZIkSZI0aSOL8gyR4eqtJEmSJKlrHKGUJEmSpG5xyqskSZIkaUpclEeSJEmSNGkJzBquEcrhSp8lSZIkSV3jCKUkSZIkdYtTXiVJkiRJU+KiPJIkSZKkycvQjVAOV28lSZIkSV3jCKUkSZIkdUMYulVeTSglSZIkqVuG7B5Kp7xKkiRJkqbEEUpJkiRJ6pYhW5THhFKSJEmSuiHxHkpJkiRJ0hQN2QjlcPVWkiRJktQ1qaoVHcMKleRA4MB158w57JVz9+z4vNlbbs59117fk/KDWnc/xWI/+7vuforFfs6sWAa17n6KxX7OrFjsZ3/X3U+x9FM/Pzj/3Iuqam7HlfeRuY/fon7xX2+ZVh0r//3rB6r/Qz/ltarOAs56zFrrHHbH/J92fN6cffakV+UHte5+isV+9nfd/RSL/ZxZsQxq3f0Ui/2cWbHYz/6uu59i6ad+DrYM3ZTXoU8oJUmSJKkrwtAtyjNc6bMkSZIkqWscoZQkSZKkbnHKqyRJkiRpSjJcU15NKCVJkiSpKwKzhmuEcrh6K0mSJEnqGkcoJUmSJKkbglNeJUmSJElT5KI8kiRJkqTJy9CNUA5X+ixJkiRJ6hpHKCVJkiSpW4ZslVcTSkmSJEnqhiFclGe40mdJkiRJUtc4QilJkiRJXRFXeZUkSZIkTdGQTXk1oZQkSZKkbhmyEcrh6q0kSZIkqWscoZQkSZKkbkhgllNeJUmSJElTMWRTXk0oJUmSJKlbhmxRnp6lz0mOTrIoySVJFibZvdl/ZJI1etVuW/sPNO0uTPKNXrcnSZIkScOmJyOUSfYADgB2rap7k2wAzG4OHwl8DrirF223ubuqdu5xG5IkSZLUGL7nUPaqtxsDS6rqXoCqWlJVNyR5A7AJcF6S8wCSnJTkwmY085iRCpI8O8llSX6c5PgkZzf710xyWpILkixIclCP+iBJkiRJk5JkWq9B06uE8lxg8yRXJPlYkr0Bqup44AZgXlXNa8oeXVVzgZ2AvZPslGQ14BRg/6p6GrBhW91HA9+vqt2AecCxSdYcI4bVmkT150meO1aQSQ5vylx41/33daHbkiRJkoZWaI1QTuc1YHoScVXdATwZOBz4I3BGkkPHKX5wkouBBcCOwA7A9sDVVXVNU+aLbeX3BY5KshCYD6wGbDFGvVs0ieo/Ah9O8rgx4jy1quZW1dw1Vpn9yBokSZIkSePqWQpcVQ9U1fyqeifwOuB5o8sk2Qp4M/CsqtoJ+CatBHGisd4Az6uqnZvXFlV16Rjt39D8eTWtxHOX6fZJkiRJksaX5TJCmWS/JJcnuSrJUWMcf0mzOOolSX6a5Eld72qjJwllku2SbNO2a2fguub97cBazfu1gTuB25JsBOzf7L8M2DrJls32C9vqOgd4fZoJxkkekSgmWS/Jqs37DYC9gN9Ms1uSJEmSNLFZmd5rGZKsBJxIK3faAXhxkh1GFbsG2LsZtHsPcGqXe/kXvXoO5RzghCTrAkuBq2hNf4VWZ76d5MaqmpdkAbAIuBr4CUBV3Z3kNcB3kiwBzm+r+z3Ah4FLmqTyWloryrZ7AnBKkgdpJc0fqCoTSkmSJEmD7inAVc1MTJJ8CTiItgG0qvppW/mfA5v1KpieJJRVdRGw5zjHTgBOaNs+dJxqzquq7Zuk8UTgwqb83cCrl9H+T4G/mnzkkiRJkjQN019YZ4MkF7Ztn1pV7SOMmwLXt20vBnafoL5XAt+eblDj6dUIZTccluQQWs+vXEBr1VdJkiRJ6k8Bpv/ojyXN4qITtTJajVkwmUcroXzadIMaT98mlFV1HHDcio5DkiRJkjqT5fHoj8XA5m3bm9F6NOPDI0l2Aj5B61GMN/cqmMF70IkkSZIkDa8LgG2SbJVkNvAi4BvtBZJsAXwVeGlVXdHLYPp2hFKSJEmSBs70p7xOqKqWJnkdradfrAScVlWLkhzRHD8Z+HfgUcDHmodjLF3GNNopM6GUJEmSpG7p/ZRXqupbwLdG7Tu57f2rgFf1PBBMKCVJkiSpO9LZsyRnEu+hlCRJkiRNiSOUkiRJktQty2HKaz8xoZQkSZKkbunxojz9xoRSkiRJkrpiuTyHsq8MV28lSZIkSV3jCKUkSZIkdYtTXiVJkiRJkxaGbsqrCaUkSZIkdUVg1nAllMPVW0mSJElS1zhCKUmSJEldEu+hlCRJkiRNyZDdQzlcvZUkSZIkdY0jlJIkSZLUDWHoHhuSqlrRMaxQSQ4EDlx3zpzDXjl3z47Pm73l5tx37fU9KT+odfdTLPazv+vup1js58yKZVDr7qdY7OfMisV+9nfd/RRLP/Xzg/PPvaiq5nZceR+Z+1c71AVf++y06pi1zdyB6v/Qj1BW1VnAWY9Za53D7pj/047Pm7PPnvSq/KDW3U+x2M/+rrufYrGfMyuWQa27n2KxnzMrFvvZ33X3Uyz91M+BN2QjlN5DKUmSJEmakqEfoZQkSZKkrpk1XGN2JpSSJEmS1A3J0E15NaGUJEmSpG7xOZSSJEmSJC2bI5SSJEmS1C1OeZUkSZIkTY0JpSRJkiRp0oZvUR7voZQkSZIkTYkjlJIkSZLULUM2QmlCKUmSJEldM1wJpVNeJUmSJElT4gilJEmSJHVDcMqrJEmSJGmKhiufNKGUJEmSpO4ZrozSeyglSZIkSVPiCKUkSZIkdUW8h1KSJEmSNEUmlJIkSZKkqRmuhNJ7KCVJkiRJU9KzhDLJ0UkWJbkkycIkuzf7j0yyRq/abWt/iyTnJrk0yW+SbNnrNiVJkiQNuWR6rwHTkymvSfYADgB2rap7k2wAzG4OHwl8DrirF223+Qzw3qr6bpI5wIM9bk+SJEnS0Bu8pHA6ejVCuTGwpKruBaiqJVV1Q5I3AJsA5yU5DyDJSUkubEYzjxmpIMmzk1yW5MdJjk9ydrN/zSSnJbkgyYIkB41uPMkOwMpV9d2m/TuqqtcJrCRJkqRhNt3RyQEcoexVQnkusHmSK5J8LMneAFV1PHADMK+q5jVlj66qucBOwN5JdkqyGnAKsH9VPQ3YsK3uo4HvV9VuwDzg2CRrjmp/W+BPSb7aJJ3HJllpdJBJDm+S2Qvvuv++LnZfkiRJkma+niSUVXUH8GTgcOCPwBlJDh2n+MFJLgYWADsCOwDbA1dX1TVNmS+2ld8XOCrJQmA+sBqwxag6VwaeDrwZ2A3YGnhE+1V1alXNraq5a6wye/RhSZIkSZqcIRuh7NljQ6rqAVoJ3/wkvwIOAU5vL5NkK5qkr6puTXI6rQRxok8ywPOq6vIJyiwGFlTV1U07XweeCnxyKn2RJEmSpM4MXlI4HT0ZoUyyXZJt2nbtDFzXvL8dWKt5vzZwJ3Bbko2A/Zv9lwFbt63M+sK2us4BXp+00vcku4wRwgXAeklGpso+E/jNlDskSZIkSXqEXo1QzgFOSLIusBS4itb0V4BTgW8nubGq5iVZACwCrgZ+AlBVdyd5DfCdJEuA89vqfg/wYeCSJqm8ltaKsn9RVQ8keTPwvabMRcDHe9FRSZIkSRqRAZy2Oh09SSir6iJgz3GOnQCc0LZ96DjVnFdV2zcJ4YnAhU35u4FXdxDDd2kt9CNJkiRJy8eQJZS9WuW1Gw5rFt5ZBKxDa9VXSZIkSepT6cJrsPRsUZ7pqqrjgONWdBySJEmSpLH1bUIpSZIkSQNnyKa8mlBKkiRJUjcEE0pJkiRJ0lQNV0LZz4vySJIkSZL6mCOUkiRJktQtTnmVJEmSJE3JcOWTJpSSJEmS1B2D+SzJ6fAeSkmSJEnSlDhCKUmSJEnd4j2UkiRJkqRJ8zmUkiRJkqSpG66E0nsoJUmSJElT4gilJEmSJHWLU14lSZIkSZOXoUsonfIqSZIkSQMkyX5JLk9yVZKjxjieJMc3xy9JsmuvYjGhlCRJkqSuyTRfy6g9WQk4Edgf2AF4cZIdRhXbH9imeR0OnDTNTo3LhFKSJEmSuiWZ3mvZngJcVVVXV9V9wJeAg0aVOQj4TLX8HFg3ycbd7WhLqqoX9Q6MJAcCBwIvAS4do8gGwJIx9q8D3DaJpiZTflDr7qdYxivr9eyPursVSzeu5yD0s9/r7lYs/X49B+Ez7Ke6vZ79EYvXs7/rXlGxjHU9+6mf21TVOpOou28k+Q6tz3c6VgPuads+tapObWvj+cB+VfWqZvulwO5V9bq2MmcDH6iqHzfb3wPeWlUXTjO2R6oqX62k+tRx9l84mfKTrX8m1d1PsXg9+7vufrqeg9DPfq97WK7nIHyG/VS317M/YvF69nfd/XQ9B7mfw/YCXgB8om37pcAJo8p8E3ha2/b3gCf3Ih6nvD7krD4qP6h1T7b8oNY92fLWPf3yg1r3ZMsPat2TLW/d0y8/qHVPtvyg1j3Z8oNa92TLW/f0yw9q3ZMtP9m6h81iYPO27c2AG6ZQpiuGfsrrsiS5sKrmrug41B1ez5nF6zmzeD1nFq/nzOL1nFm8noMtycrAFcCzgN8BFwD/WFWL2sr8HfA64NnA7sDxVfWUXsTjcyiX7dRlF9EA8XrOLF7PmcXrObN4PWcWr+fM4vUcYFW1NMnrgHOAlYDTqmpRkiOa4ycD36KVTF4F3AW8vFfxOEIpSZIkSZoS76GUJEmSJE2JCaUkSZIkaUpMKCeQZL8klye5KslRKzoeTU6S05LclOTXbfvWT/LdJFc2f663ImNUZ5JsnuS8JJcmWZTkX5r9Xs8BlGS1JOcn+WVzPY9p9ns9B1iSlZIsaJ595vUcYEmuTfKrJAuTXNjs83oOqCTrJvlKksua36N7eD3VTSaU40iyEnAisD+wA/DiJDus2Kg0SacD+43adxTwvarahtbzePyHgsGwFHhTVT0BeCrw2ub/R6/nYLoXeGZVPQnYGdgvyVPxeg66fwEubdv2eg62eVW1c9tKoF7PwfUR4DtVtT3wJFr/n3o91TUmlON7CnBVVV1dVfcBXwIOWsExaRKq6ofALaN2HwR8unn/aeC5yzMmTU1V3VhVFzfvb6f1y3BTvJ4DqVruaDZXaV6F13NgJdkM+DvgE227vZ4zi9dzACVZG3gG8EmAqrqvqv6E11NdZEI5vk2B69u2Fzf7NNg2qqoboZWkAI9ewfFokpJsCewC/AKv58BqpkcuBG4CvltVXs/B9mHgLcCDbfu8noOrgHOTXJTk8Gaf13MwbQ38EfhUMyX9E0nWxOupLjKhHF/G2OczVqQVKMkc4L+BI6vqzys6Hk1dVT1QVTsDmwFPSfLEFRySpijJAcBNVXXRio5FXbNXVe1K67af1yZ5xooOSFO2MrArcFJV7QLcidNb1WUmlONbDGzetr0ZcMMKikXd84ckGwM0f960guNRh5KsQiuZ/HxVfbXZ7fUccM3Uq/m07nf2eg6mvYDnJLmW1u0hz0zyObyeA6uqbmj+vAn4Gq3bgLyeg2kxsLiZBQLwFVoJptdTXWNCOb4LgG2SbJVkNvAi4BsrOCZN3zeAQ5r3hwD/swJjUYeShNb9H5dW1YfaDnk9B1CSDZOs27xfHfhr4DK8ngOpqt5WVZtV1Za0fld+v6r+Ca/nQEqyZpK1Rt4D+wK/xus5kKrq98D1SbZrdj0L+A1eT3VRqpzFOZ4kz6Z1X8hKwGlV9d4VG5EmI8kXgX2ADYA/AO8Evg6cCWwB/BZ4QVWNXrhHfSbJ04AfAb/ioXu03k7rPkqv54BJshOtRSBWovUPm2dW1buTPAqv50BLsg/w5qo6wOs5mJJsTWtUElrTJb9QVe/1eg6uJDvTWjBrNnA18HKa7168nuoCE0pJkiRJ0pQ45VWSJEmSNCUmlJIkSZKkKTGhlCRJkiRNiQmlJEmSJGlKTCglSZIkSVNiQilJAy7JHZMsv0+Ss7vQ7nOSHDXJcx5IsrDtteV04+gHzWd6W5IFSS5P8sMkByyHdj+RZIdetyNJ0nhWXtEBSJIGU1V9g9bDsSfj7qraeawDSULrcVYPjnV8APyoqg6Avzz37etJ7q6q7/Wqwap6Va/qliSpE45QStIM0YySzU/ylSSXJfl8k6SRZL9m34+Bf2g7Z80kpyW5oBldO6jZf3ySf2/e/20z4jZrVHuHJvlo8/705pyfJrk6yfM7jHnLJJcm+RhwMbB5kn9r4rkkyTFtZY9uRv/+N8kXk7y52T8/ydzm/QZJrm3er5Tk2La6Xt3B57Rb04dfJjk/yVpJftQkiCNx/CTJThP1q6oWAu8GXtec89gk32vi+F6SLdo+t5OSnNd8bns31+PSJKe3tXlSkguTLBr1mbT3/Y4k721i/3mSjTq5BpIkTYcJpSTNLLsARwI7AFsDeyVZDfg4cCDwdOAxbeWPBr5fVbsB84Bjk6wJHAW8MMk84Hjg5R2MHG4MPA04APjAOGVWb5vu+rVm33bAZ6pql+b9NsBTgJ2BJyd5RpInAy9q+vcPwG4dfBavBG5r+rYbcFiSrZpjY31Os4EzgH+pqicBfw3cDXwCOBQgybbAqlV1SQftXwxs37z/aNPHnYDP0/pMR6wHPBN4I3AWcBywI/BXbYns0VU1F9gJ2HuchHZN4OdN7D8EDusgRkmSpsWEUpJmlvOranGT/C0EtqSV1FxTVVdWVQGfayu/L3BUkoXAfGA1YIuquotWQvJd4KNV9X8dtP31qnqwqn4DjDc6dndV7dy8/r7Zd11V/bwtnn2BBTyUkG1DKxH+WlXdVVV/prOptvsCL2v69gvgUU1dMPbntB1wY1VdAFBVf66qpcCXgQOSrAK8Aji9g7YB0vZ+D+ALzfvP0kq8R5zVXJdfAX+oql81cS1q4gI4OMnFtD6XHWklwqPdB4zcG3tR27mSJPWM91BK0sxyb9v7B3joe77GKR/geVV1+RjH/gq4GdhkCm1n3FKPdOeo895fVac8LMjkSMbvw1Ie+gfS1UbV9fqqOmdUXfsw9ueUsdqoqruSfBc4CDgYmDthbx6yC3DpOMfa2xmJ5cFRcT0IrNyMqr4Z2K2qbm2mwrb3c8T9TWIKD7/2kiT1jCOUkjTzXQZsleRxzfaL246dA7y+7R7CXZo/Hwu8iVZStH+S3ZdTrOcAr0gyp4lj0ySPpjWF8++TrJ5kLVrTd0dcCzy5ef/8UXX9czOySJJtm+m847kM2CTJbk35tZKMJGWfoDVN9YKqumVZnWimpP5/wInNrp/SmrIL8BLgx8uqo83atJLu25r7IvefxLmSJPWU/3opSTNcVd2T5HDgm0mW0Epmntgcfg/wYeCSJqm8NsmBwCeBN1fVDUleCZyeZLequqfHsZ6b5AnAz5oc9w7gn6rq4iRn0Jqeeh3wo7bT/gs4M8lLge+37f8ErWmfFzd9+yPw3Anavi/JC4ETkqxO6/7JvwbuqKqLkvwZ+NQE4T89yQJgDeAm4A1tK7y+ATgtyb81cbx8mR/GQ3H9sql3EXA18JNOz5Ukqdfy0OwYSZIGQ5J30Ur0/ms5tbcJrXtMtx/gx5pIktR1TnmVJGkCSV5Ga1Gfo00mJUl6OEcoJUmSJElT4gilJEmSJGlKTCglSZIkSVNiQilJkiRJmhITSkmSJEnSlJhQSpIkSZKm5P8Hh8O8ILMhESAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generation process visualization saved as 'gmt_generation_process.png'\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Rectangle\n",
    "import time\n",
    "from functools import lru_cache\n",
    "import math\n",
    "\n",
    "# === 1. GMT-FFT 核心实现（带路径追踪与剪枝）===\n",
    "@lru_cache(maxsize=1024)\n",
    "def get_twiddle_cached(N, stage, m, W_step):\n",
    "    \"\"\"\n",
    "    带缓存的旋转因子计算\n",
    "    参数：N: 总长度, stage: 当前层, m: 块内索引, W_step: 步长\n",
    "    \"\"\"\n",
    "    k = m * W_step\n",
    "    return np.exp(-2j * np.pi * k / N)\n",
    "\n",
    "def gmt_fft_sparse_with_trace(x, threshold=1e-10):\n",
    "    \"\"\"\n",
    "    GMT-FFT：带路径追踪的稀疏版本\n",
    "    返回：X（结果） + trace（每层活跃索引）\n",
    "    \"\"\"\n",
    "    N = len(x)\n",
    "    X = np.array(x, dtype=complex)\n",
    "    \n",
    "    if (N & (N-1)) != 0:\n",
    "        raise ValueError(\"N must be a power of 2\")\n",
    "    \n",
    "    M = N.bit_length() - 1  # log2(N)\n",
    "    \n",
    "    # 存储每层的活跃索引（用于可视化）\n",
    "    trace = [set() for _ in range(M + 1)]  # +1 包括初始层\n",
    "    \n",
    "    # --- 初始层：位逆序置换 + 活跃索引 ---\n",
    "    for i in range(N):\n",
    "        j = int(f\"{i:0{M}b}\"[::-1], 2)\n",
    "        if j > i:\n",
    "            X[i], X[j] = X[j], X[i]\n",
    "        if abs(X[i]) > threshold:\n",
    "            trace[0].add(i)\n",
    "    \n",
    "    # --- 按层进行蝶形运算（带剪枝）---\n",
    "    for stage in range(M):\n",
    "        span = 1 << stage\n",
    "        W_step = N // (1 << (stage + 1))\n",
    "        active_next = set()\n",
    "        \n",
    "        for k in range(0, N, 1 << (stage + 1)):\n",
    "            for m in range(span):\n",
    "                i1 = k + m\n",
    "                i2 = i1 + span\n",
    "                \n",
    "                # 剪枝：若两个输入都不活跃，则跳过\n",
    "                if i1 not in trace[stage] and i2 not in trace[stage]:\n",
    "                    continue\n",
    "                \n",
    "                active_next.add(i1)\n",
    "                active_next.add(i2)\n",
    "                \n",
    "                W = get_twiddle_cached(N, stage, m, W_step)\n",
    "                t = W * X[i2]\n",
    "                u = X[i1]\n",
    "                X[i1] = u + t\n",
    "                X[i2] = u - t\n",
    "        \n",
    "        trace[stage + 1] = active_next\n",
    "    \n",
    "    return X, trace\n",
    "\n",
    "# === 2. 传统FFT（用于对比）===\n",
    "def traditional_fft(x):\n",
    "    \"\"\"\n",
    "    传统迭代FFT，无任何剪枝\n",
    "    用于与GMT-FFT进行公平对比\n",
    "    \"\"\"\n",
    "    N = len(x)\n",
    "    X = np.array(x, dtype=complex)\n",
    "    \n",
    "    if (N & (N-1)) != 0:\n",
    "        raise ValueError(\"N must be a power of 2\")\n",
    "    \n",
    "    M = N.bit_length() - 1\n",
    "    \n",
    "    # 位逆序置换\n",
    "    for i in range(N):\n",
    "        j = int(f\"{i:0{M}b}\"[::-1], 2)\n",
    "        if j > i:\n",
    "            X[i], X[j] = X[j], X[i]\n",
    "    \n",
    "    # 所有层全部计算，无剪枝\n",
    "    for stage in range(M):\n",
    "        span = 1 << stage\n",
    "        W_step = N // (1 << (stage + 1))\n",
    "        \n",
    "        for k in range(0, N, 1 << (stage + 1)):\n",
    "            for m in range(span):\n",
    "                i1 = k + m\n",
    "                i2 = i1 + span\n",
    "                W = np.exp(-2j * np.pi * m * W_step / N)\n",
    "                t = W * X[i2]\n",
    "                u = X[i1]\n",
    "                X[i1] = u + t\n",
    "                X[i2] = u - t\n",
    "    \n",
    "    return X\n",
    "\n",
    "# === 3. 性能对比实验 ===\n",
    "def run_performance_comparison():\n",
    "    \"\"\"\n",
    "    对不同稀疏度K进行对比实验\n",
    "    \"\"\"\n",
    "    N = 1024\n",
    "    K_list = [1, 2, 4, 8, 16, 32, 64, 128]\n",
    "    \n",
    "    times_gmt = []\n",
    "    times_trad = []\n",
    "    errors = []\n",
    "    speedups = []\n",
    "    \n",
    "    print(\"Starting FFT Comparison Experiment...\")\n",
    "    print(f\"Signal Length N = {N}\")\n",
    "    print(\"-\" * 60)\n",
    "    \n",
    "    for K in K_list:\n",
    "        x = np.zeros(N)\n",
    "        indices = np.random.choice(N, size=K, replace=False)\n",
    "        x[indices] = 1.0\n",
    "        \n",
    "        # 传统FFT\n",
    "        start = time.time()\n",
    "        X_trad = traditional_fft(x)\n",
    "        t_trad = time.time() - start\n",
    "        \n",
    "        # GMT-FFT\n",
    "        start = time.time()\n",
    "        X_gmt, _ = gmt_fft_sparse_with_trace(x)\n",
    "        t_gmt = time.time() - start\n",
    "        \n",
    "        error = np.max(np.abs(X_trad - X_gmt))\n",
    "        \n",
    "        times_trad.append(t_trad)\n",
    "        times_gmt.append(t_gmt)\n",
    "        errors.append(error)\n",
    "        speedups.append(t_trad / t_gmt if t_gmt > 0 else np.inf)\n",
    "        \n",
    "        print(f\"K={K:3d} | Trad: {t_trad:.6f}s | GMT: {t_gmt:.6f}s | \"\n",
    "              f\"Speedup: {t_trad/t_gmt:4.2f}x | Error: {error:.2e}\")\n",
    "    \n",
    "    # === 绘图 ===\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "    \n",
    "    ax1.plot(K_list, times_trad, 's-', label='Traditional FFT', color='red')\n",
    "    ax1.plot(K_list, times_gmt, 'o-', label='GMT-FFT (Pruned)', color='blue')\n",
    "    ax1.set_xlabel('Sparsity K (Number of Non-zeros)')\n",
    "    ax1.set_ylabel('Execution Time (seconds)')\n",
    "    ax1.set_title('Execution Time vs Sparsity')\n",
    "    ax1.set_xscale('log')\n",
    "    ax1.set_yscale('log')\n",
    "    ax1.legend()\n",
    "    ax1.grid(True, alpha=0.3)\n",
    "    \n",
    "    ax2.plot(K_list, speedups, 'd-', color='green')\n",
    "    ax2.set_xlabel('Sparsity K (Number of Non-zeros)')\n",
    "    ax2.set_ylabel('Speedup (Traditional / GMT)')\n",
    "    ax2.set_title('Speedup of GMT-FFT over Traditional FFT')\n",
    "    ax2.set_xscale('log')\n",
    "    ax2.axhline(y=1.0, color='gray', linestyle='--', alpha=0.7)\n",
    "    ax2.grid(True, alpha=0.3)\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('fft_comparison_results.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "    \n",
    "    print(\"-\" * 60)\n",
    "    print(f\"Max Error across all tests: {max(errors):.2e}\")\n",
    "    print(f\"Peak Speedup: {max(speedups):.2f}x\")\n",
    "    print(\"Figure saved as 'fft_comparison_results.png'\")\n",
    "\n",
    "# === 4. 执行过程可视化 ===\n",
    "def visualize_generation_process():\n",
    "    \"\"\"\n",
    "    可视化 GMT-FFT 的生成过程\n",
    "    显示每一层的活跃路径（热力图）\n",
    "    \"\"\"\n",
    "    N = 64  # 小一点，便于可视化\n",
    "    M = int(np.log2(N))\n",
    "    \n",
    "    # 创建稀疏信号：K=3\n",
    "    x = np.zeros(N)\n",
    "    spike_positions = [5, 20, 45]\n",
    "    x[spike_positions] = 1.0\n",
    "    \n",
    "    # 运行带追踪的 GMT-FFT\n",
    "    _, trace = gmt_fft_sparse_with_trace(x)\n",
    "    \n",
    "    # 创建热力图矩阵\n",
    "    heatmap = np.zeros((M + 1, N))\n",
    "    for stage in range(M + 1):\n",
    "        for idx in trace[stage]:\n",
    "            heatmap[stage, idx] = 1.0\n",
    "    \n",
    "    # 绘图\n",
    "    fig, ax = plt.subplots(figsize=(14, 6))\n",
    "    im = ax.imshow(heatmap, cmap='Reds', aspect='auto', interpolation='none')\n",
    "    \n",
    "    # 设置坐标轴\n",
    "    ax.set_xlabel('Index in Frequency Domain')\n",
    "    ax.set_ylabel('Generation Stage')\n",
    "    ax.set_title('GMT-FFT: Generation Process Visualization\\n(Red = Active Index)')\n",
    "    \n",
    "    # 添加颜色条\n",
    "    cbar = plt.colorbar(im, ax=ax)\n",
    "    cbar.set_label('Activity Level')\n",
    "    \n",
    "    # 标记初始非零位置（在时域）\n",
    "    for pos in spike_positions:\n",
    "        ax.text(pos, 0, f'X{pos}', ha='center', va='center', color='blue', fontsize=10, fontweight='bold')\n",
    "    \n",
    "    # 添加网格线\n",
    "    ax.set_xticks(np.arange(-0.5, N, 1), minor=True)\n",
    "    ax.set_yticks(np.arange(-0.5, M+1, 1), minor=True)\n",
    "    ax.grid(which='minor', color='gray', linestyle='-', linewidth=0.5)\n",
    "    \n",
    "    # 设置主刻度标签\n",
    "    ax.set_yticks(range(M + 1))\n",
    "    ax.set_yticklabels([f'Stage {i}' for i in range(M + 1)])\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('gmt_generation_process.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "    \n",
    "    print(\"Generation process visualization saved as 'gmt_generation_process.png'\")\n",
    "\n",
    "# === 5. 运行所有实验 ===\n",
    "if __name__ == \"__main__\":\n",
    "    # 运行性能对比\n",
    "    run_performance_comparison()\n",
    "    \n",
    "    # 运行生成过程可视化\n",
    "    visualize_generation_process()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "内存分析"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "测量内存消耗中...\n",
      "K    Trad (MB)    GMT (MB)     Diff (MB)   \n",
      "1    0.16         0.34         0.18        \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-4-b6a2ab5452a8>:99: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[idx] = np.random.randn(K) + 1j * np.random.randn(K)\n",
      "<ipython-input-4-b6a2ab5452a8>:33: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[k + j] = u + t\n",
      "<ipython-input-4-b6a2ab5452a8>:34: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[k + j + m // 2] = u - t\n",
      "<ipython-input-4-b6a2ab5452a8>:76: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[i1] = u + t\n",
      "<ipython-input-4-b6a2ab5452a8>:77: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[i2] = u - t\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2    0.16         0.29         0.13        \n",
      "4    0.18         0.28         0.10        \n",
      "8    0.18         0.39         0.21        \n",
      "16   0.18         0.44         0.26        \n",
      "32   0.18         0.67         0.49        \n",
      "64   0.04         0.68         0.64        \n",
      "128  0.18         0.83         0.65        \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ThinkPad\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:238: RuntimeWarning: Glyph 65306 missing from current font.\n",
      "  font.set_text(s, 0.0, flags=flags)\n",
      "C:\\Users\\ThinkPad\\anaconda3\\lib\\site-packages\\matplotlib\\backends\\backend_agg.py:201: RuntimeWarning: Glyph 65306 missing from current font.\n",
      "  font.set_text(s, 0, flags=flags)\n"
     ]
    },
    {
     "data": {
      "image/png": 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uy5gxY4iIRoejjchMVqxYwdKlSxk7dmyjw5EkSerQgJhi8fzzz7P99tubHPdxEcH222/vSL8kSerTBkSCDJgc9xO+TpIkqa8bMAmyJEmS1BsGZILcvHMxF7m3bs07j+m0vZUrV3LhhRe+7Lgvu+wyTjnlFADmzJnD5Zdf3rr+0Ucfba33gQ98gCVLlrzs9jbWdvv1O+ywAxMmTGDChAkcd9xxABx//PGMHTu2df2ZZ57Zev+Vr3wlo0ePbl1es2ZNr8YqSZJUSwPiIL32lj38EGcterLXtvfJiS+5AmEbGxLkk08++SVl69evZ8iQIZvc5kknndR6/7LLLmOPPfbgVa96FQAXX3zxJm/v5TjqqKM4//zzX7L+nHPO4cgjj2xd/sxnPgPArFmz2GabbTj11FPrFqMkSVJvGZAjyPV2+umn86c//YkJEyZw2mmncdNNN3HggQdy7LHHsueeewJw+OGHs/fee7P77rtz0UUXtT720ksv5XWvex37778/v/nNb1rXz5o1iy9/+ctcddVV3Hrrrbz3ve9lwoQJPPfccxxwwAGtl9u+4oor2HPPPdljjz34xCc+0fr4bbbZhjPOOIPx48czZcoUHn/8cQB+8pOfsO+++/KGN7yBlpaW1vWSJEkqmCD3gi9+8Yu85jWvYfHixZxzzjkA/O53v+MLX/hC61SISy65hN///vfceuutnHfeeaxYsYLHHnuMz3zmM/zmN7/h+uuv73DaxJFHHsmkSZP47ne/y+LFi9lyyy1byx599FE+8YlP8Itf/ILFixezcOFCfvSjHwGwevVqpkyZwm233cZ+++3HN7/5TQDe/OY3s2DBAv7whz9w9NFH86UvfanL5/f973+/dbrEpZde2rr+tNNOa11/xx139Lj/JEmS+pIBOcWiL5g8eXKbc/2ed955XH311QA88sgj3HffffzlL3/hgAMOYIcdiikcRx11FH/84x+73cbChQvbPP69730vN998M4cffjibb74573znOwHYe++9uf7664HinNFHHXUUjz32GGvWrOnW+Yi7O8VCkiRpIHAEuUa23nrr1vs33XQTN9xwA/Pnz+e2227jDW94Q+u5gF/Oac8yc6Nlw4YNa932kCFDWLduHQDTp0/nlFNO4Y477uAb3/iG5ySWJElqxwS5F2y77bY888wzGy1/+umn2W677dhqq6245557WLBgAQD77rsvN910EytWrGDt2rX84Ac/2KTt77vvvvzqV79i+fLlrF+/niuuuIL999+/01iffvppRo8eDcC3v/3t7j5FSZKkQWNATrEY/eqduzzzxKZurzPbb789b3rTm9hjjz045JBDeMc73tGm/OCDD2bOnDnstddevP71r2fKlCkA7LjjjsyaNYupU6ey4447MnHiRNavX/+S7R9//PGcdNJJbLnllsyfP791/Y477shZZ53FgQceSGby9re/ncMOO6zTWGfNmsV73vMeRo8ezZQpU/jzn//c3W6QJEkaFKKzn+n7okmTJuWGMzhscPfdd/MP//APDYpIm8rXS5Kkvm1MczMPLVtWt/Z2Hj2aB5curVt7G0TE7zNzUvv1A3IEWZIkST330LJlrJw1q27tNdWxre5wDrIkSZJUYYIsSZIkVZggS5IkSRUmyJIkSVKFCbIkSZJUMSAT5DHNzUREr93GNDd3q93HH3+cY489ll122YW9996bqVOncvXVV3PTTTcREXzrW99qrfuHP/yBiODLX/4yH/7wh5kwYQLjxo1jyy23ZMKECUyYMIGrrrqq7fMaM4Y999yztfyWW27hwQcfbPOYCRMmcOaZZ7beHzJkSOv98847r1f7WZIkaSAakKd56+1Tk3Tn1COZyeGHH8773vc+vve97xVxPPQQc+fOZbvttmPPPffk+9//Pu9///sBuPLKKxk/fjwAF1xwAQAPPvgg73znO1m8ePFG2/nlL3/JqFGjWpcffPBBXvOa17zkMZ/5zGcA2GabbTrdniRJktoakCPIjfCLX/yCzTffnJNOOql13c4778z06dMBePWrX83zzz/P448/Tmbys5/9jEMOOaRR4UqSJGkjapogR8TBEXFvRNwfEad3UD4yIn4SEbdFxF0RcUIt46mlu+66i4kTJ3Za58gjj+QHP/gBt9xyCxMnTmSLLbbY5HYOPPBAJkyYwL777tu67k9/+lPrNIoPf/jDm7xNSZIk/U3NplhExBDgAuCtwFJgYUTMzcwllWofBpZk5qERsQNwb0R8NzPX1Cquevnwhz/Mr3/9azbffHPOOeccAP75n/+Zo446invuuYdjjjmGW265ZZO3236KBdDhFAtJkiT1TC1HkCcD92fmA2XCeyVwWLs6CWwbEQFsA/wVWFfDmGpm9913Z9GiRa3LF1xwATfeeCNPPvlk67pXvvKVDBs2jOuvv563vOUtnW5v/fr1raPCn/70p2sWtyRJktqq5UF6o4FHKstLgX3b1TkfmAs8CmwLHJWZL7bfUEScCJwI0NzczPLly9uUr1+/nrVr1/Ze5B3oavvTpk3jueee4/zzz+eDH/wgAE8//TQA69atIzNZu3Ytn/70p3niiSd48cUXWb9+fZvY165d21oPYOHChS9pf+3atW1iaf+YnsReb+vXr3/JayhJkvqOcePGsXLrrevaXl/KDWqZIEcH67Ld8j8Ci4GDgNcA10fEvMxc1eZBmRcBFwFMmjQp208xePLJJxk2bFjr8s6jR3frzBPdtfPo0W22vzE//vGPmTlzJl/5ylfYYYcd2HrrrTn77LMZOnQoEcGwYcPYb7/9WusPGTKEIUOGtG572LBhrfU2ZtiwYW3Ku/uYvmTIkCEvmSYiSZL6jiVLltC0enVd2+tLuUEtE+SlwE6V5WaKkeKqE4AvZmYC90fEn4HdgN+9nIYfXLr05Ty8x3bccUeuvPLKDssOOOCAl6yb1S6JHzNmDHfeeedGt//ggw++ZF1Xj3n22Wc3WiZJkqSXquUc5IXArhExNiI2B46mmE5R9TDwFoCI+Hvg9cADNYxJkiRJ6lTNRpAzc11EnAJcBwwBLsnMuyLipLJ8DvA54LKIuINiSsYnMrPvTECRJEnSoFPTK+ll5rXAte3WzancfxR4Wy+1RXEyDPVlxWwaSZKkvmtAXElv+PDhrFixwuSrj8tMVqxYwfDhwxsdiiRJ0kbVdAS5Xpqbm1m6dGmbcw6rbxo+fDjNzc2NDkOSJGmjBkSCPGzYMMaOHdvoMCRJkjQADIgpFpIkSVJvMUGWJEmSKkyQJUmSpAoTZEmSJKnCBFmSJEmqMEGWJEmSKkyQJUmSpAoTZEmSJKnCBFmSJEmqMEGWJEmSKkyQJUmSpAoTZEmSJKnCBFmSJEmqMEGWJEmD2syZM5k2bRozZsxos/6jH/0oBxxwAAcccADbbbddg6JTI5ggS5KkQWvRokWsXr2aefPmsWbNGhYuXNha9vWvf52bbrqJr33ta7zjHe9oYJSqNxNkSZI0aM2fP5+WlhYAWlpaWLBgwUvqXH311bz73e+ud2hqIBNkSZI0aK1cuZIRI0YAMHLkSJ566qmX1PnZz37GwQcfXO/Q1EAmyJIkadBqampi1apVAKxatYqmpqY25ffddx+jR49mq622akB0ahQTZEmSBggPNtt0U6dO5cYbbwTghhtuYMqUKW3Kr776ao444ohGhKYGMkGWJGkA8GCznpk4cSLDhw9n2rRpbLbZZkyePJnp06e3ll9zzTUceuihDYxQjTC00QFIkqSXr6ODzfbZZ582dTzYrGPnnntum+XZs2e33r/55pvrHY76AEeQJUkaADzYTOo9JsiSJA0AHmwm9R4TZEmSBgAPNpN6jwmyJEkDgAebSb3Hg/QkSRogPNhM6h2OIEuSJEkVJsiSJElShQmyJEmSVGGCLEmSJFXUNEGOiIMj4t6IuD8iTu+g/LSIWFze7oyI9RHxd7WMSZIkSepMzRLkiBgCXAAcAowDjomIcdU6mXlOZk7IzAnAJ4FfZeZfaxWTJEmS1JVajiBPBu7PzAcycw1wJXBYJ/WPAa6oYTySJElSl2p5HuTRwCOV5aXAvh1VjIitgIOBUzZSfiJwIkBzczPLly/v3UglSZLUaty4cazceuu6tteX8rtaJsjRwbrcSN1Dgd9sbHpFZl4EXAQwadKkHDVqVO9EKEmSpJdYsmQJTatX17W9vpTf1XKKxVJgp8pyM/DoRuoejdMrJEmS1AfUMkFeCOwaEWMjYnOKJHhu+0oRMRLYH/hxDWORJEmSuqVmUywyc11EnAJcBwwBLsnMuyLipLJ8Tln1CODnmVm/cXxJkiRpI2o5B5nMvBa4tt26Oe2WLwMuq2UckiRJUnd5JT1JkiSpwgRZkiRJqjBBliRJkipMkCVJ0oA1prmZiKjLbUxzc6OfrnpJTQ/SkyRJaqSHli1j5axZdWmrqU7tqPYcQZYkSZIqTJAlSZKkChNkSZIkqcIEWZKkfsCDzaT68SA9SZL6AQ82k+rHEWRJkiSpwgRZkiRJqjBBliRJkipMkCVJkqQKE2RJkiSpwgRZkiRJqjBBliRJkipMkCVJkqQKE2RJkiSpwgRZkiRJqjBBliRJkipMkCVJkqQKE2RJkiSpwgRZkiRJqjBBliRJkipMkCVJkqQKE2RJkiSpwgRZkiRJqjBBliRJkipMkCVJkqQKE2RJkiSpwgRZkiRJqqhpghwRB0fEvRFxf0ScvpE6B0TE4oi4KyJ+Vct4JEmSpK4MrdWGI2IIcAHwVmApsDAi5mbmkkqdJuBC4ODMfDgiXlGreCRJkqTuqOUI8mTg/sx8IDPXAFcCh7Wrcyzww8x8GCAzn6hhPJIkSVKXapkgjwYeqSwvLddVvQ7YLiJuiojfR8RxNYxHkiRJ6lLNplgA0cG67KD9vYG3AFsC8yNiQWb+sc2GIk4ETgRobm5m+fLlNQhXkqS+a9y4cazceuu6tTVQ/tfabz1Tz37b0F5f6rtaJshLgZ0qy83Aox3UWZ6Zq4HVEXEzMB5okyBn5kXARQCTJk3KUaNG1SxoSZL6oiVLltC0enXd2hoo/2vtt56pZ79taK8v9V0tp1gsBHaNiLERsTlwNDC3XZ0fA9MiYmhEbAXsC9xdw5gkSZKkTtVsBDkz10XEKcB1wBDgksy8KyJOKsvnZObdEfEz4HbgReDizLyzVjFJkiRJXanlFAsy81rg2nbr5rRbPgc4p5ZxSJIkSd3llfQkSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqhnZVISKagaOBacCrgOeAO4H/Bn6amS/WNEJJkiSpjjpNkCPiUmA0cA1wNvAEMBx4HXAwcEZEnJ6ZN9c6UEmSJKkeuhpB/kpm3tnB+juBH0bE5sCrez8sSZIkqTE6nYO8keS4Wr4mM+/v3ZAkSYPdzJkzmTZtGjNmzHhJWWYyfvx4Lr744gZEJmkw6DRBjohdI+KyiPhqRDRHxE8jYnVE3BYR+9QrSEnS4LFo0SJWr17NvHnzWLNmDQsXLmxTPnfuXF7xilc0KDpJg0FXZ7G4FLgFeBT4LXAJsD1wKnB+VxuPiIMj4t6IuD8iTu+g/ICIeDoiFpe3T2/6U5AkDSTz58+npaUFgJaWFhYsWNCm/IorruCoo45qRGiSBomuEuRtMvOizPwy8Fxm/iAzn8/M64EtOntgRAwBLgAOAcYBx0TEuA6qzsvMCeXtsz15EpKkgWPlypWMGDECgJEjR/LUU0+1ll133XXsv//+DB3a5UmYJKnHukqQq6dwW9VJWUcmA/dn5gOZuQa4EjhsE+OTJA0yTU1NrFpV/MtZtWoVTU1NrWUXX3wxJ5xwQoMikzRYdPUVfLeIuB0I4DXlfcrlXbp47GjgkcryUmDfDupNjYjbKKZxnJqZd7WvEBEnAicCNDc3s3z58i6aliT1V7vtthuXX345Bx10ENdccw1HH3106+f+3Xffzdvf/nb+8pe/kJnsvvvu7Lrrrg2OuD7GjRvHyq23rltbA+V/rf3WM/Xstw3t9aW+6ypB/oeXse3oYF22W14E7JyZz0bE24EfAS/5pMvMi4CLACZNmpSjRo16GWFJkvqyt7zlLcydO5cjjjiC8ePH87a3vY3p06cze/Zs7ryzOLnSZZddxrp165g6dWqDo62fJUuW0LR6dd3aGij/a+23nqlnv21ory/1XacJcmY+9DK2vRTYqbLcTDFKXN3+qsr9ayPiwogYlZl95yuEJKnuzj333DbLs2fPbrN8/PHH1zEaSYNNV1fSe4a2o75RLgeQmTmik4cvBHaNiLHAMorLVR/bbvuvBB7PzIyIyRRzolds8rOQJEmSeklXUyxuBF4J/BC4MjMf7u6GM3NdRJwCXAcMAS7JzLsi4qSyfA5wJPChiFgHPAccnZntp2FIkiRJddPVFIvDI2Ik8G7gmxExHPg+RbL81642npnXAte2Wzencv98unE+ZUmSJKleujrNG5n5dGZeSnE+4znAZ4HjaxyXJEmS1BBdnmk9It4IHANMA34NHJGZ82odmCRJktQIXR2k9yCwkuIiHycC68r1EwEyc1Ftw5MkSZLqq6sR5Acpzlrxj8DbaHtu4wQOqk1YkiRJUmN0dZDeAXWKQ5IkSeoTOj1ILyLe3EX5iIjYo3dDkiRJkhqnqykW/xQRXwJ+BvweeBIYDrwWOBDYGfhYTSOUJEmS6qirKRYzI2I7igt6vAfYkeKCHncD38jMX9c+REmSJKl+ujzNW2Y+BXyzvEmSJEkDWpcXCpEkSZIGExNkSaqhmTNnMm3aNGbMmPGSssxk/PjxXHzxxQ2ITJK0MSbIklQjixYtYvXq1cybN481a9awcOHCNuVz587lFa94RYOikyRtTLcS5IjYKiL+T0R8s1zeNSLeWdvQJKl/mz9/Pi0tLQC0tLSwYMGCNuVXXHEFRx11VCNCkyR1orsjyJcCLwBTy+WlwOdrEpEkDRArV65kxIgRAIwcOZKnnnqqtey6665j//33Z+jQLo+VliTVWXcT5Ndk5peAtQCZ+RxtLzstSWqnqamJVatWAbBq1Sqamppayy6++GJOOOGEBkUmSepMdxPkNRGxJZAAEfEaihFlSdJGTJ06lRtvvBGAG264gSlTprSW3XfffRx++OF85Stf4etf/zr33HNPo8KUJLXT3d/2PkNxNb2dIuK7wJuA42sVlCQNBBMnTmT48OFMmzaN8ePHM3nyZKZPn87s2bNZvHgxAJdddhnr1q1jt912a2ywkqRW3UqQM/P6iFgETKGYWjEjM5fXNDJJGgDOPffcNsuzZ89us3z88cfXMRpJUnd09ywWbwKez8z/BpqAT0XEzrUMTJI0MI1pbiYi6nIb09zc6KcrqR/q7hSL/wuMj4jxwGnAJcDlwP61CkySNDA9tGwZK2fNqktbTXVqR9LA0t2D9NZlZgKHAedl5rnAtrULS5IkSWqM7o4gPxMRnwT+BdgvIoYAw2oXliRJktQY3R1BPoritG7vz8y/AKOBc2oWlSRJktQg3T2LxV+Ar1aWH6aYgyxJkiQNKN1KkCPiGcqLhACbU0yveDYzR9YqMEmSJKkRujuC3OaAvIg4HJhci4AkSZKkRuruHOQ2MvNHwEG9G4okSZLUeN2dYvHuyuJmwCT+NuVCkiRJGjC6e5q3Qyv31wEPUpwTWZIkSRpQujsH+YRaByJJkiT1BT2ag6zGmzlzJtOmTWPGjBlt1p911lnst99+7LPPPlx99dUNik6SJKn/MkHuhxYtWsTq1auZN28ea9asYeHCha1lp556KjfffDO//OUvOfvssxsYpSRJUv9U0wQ5Ig6OiHsj4v6IOL2TevtExPqIOLKW8QwU8+fPp6WlBYCWlhYWLFjQWjZsWHEF8Oeee4499tijIfFJkiT1Z91KkCOiKSI+EhFfjYjzNty6eMwQ4ALgEGAccExEjNtIvbOB6zY9/MFp5cqVjBgxAoCRI0fy1FNPtSk/+eST2WuvvTjoIM/EJ0mStKm6O4J8LTAGuAP4feXWmcnA/Zn5QGauAa6k4zNfTAf+H/BEN2MZ9Jqamli1ahUAq1atoqmpqU35hRdeyD333MMXvvCFBkQnSZLUv3U3QR6emf+WmZdm5rc33Lp4zGjgkcry0nJdq4gYDRwBzOl2xGLq1KnceOONANxwww1MmTKlteyFF14AYMstt2wdZZYkSVL3dfc8yN+JiP8NXAO8sGFlZv61k8dEB+vaX1zk68AnMnN9REfVyw1FnAicCNDc3Mzy5cu7GfbA9OpXv5rMZMqUKey+++7ssssufOADH+CLX/wip556Kvfddx9r167l5JNPHvR9JanvGTduHCu33rpubQ2Uz0H7rWfst56pZ79taK8v9V13E+Q1wDnAGfwtyU1gl04esxTYqbLcDDzars4k4MoyOR4FvD0i1pWXsm6VmRcBFwFMmjQpR40a1c2wB66LLrqozfLFF18MwGWXXdaAaCSp+5YsWULT6tV1a2ug/M+w33rGfuuZevbbhvb6Ut91N0H+N+C1mbkpqf1CYNeIGAssA44Gjq1WyMyxG+5HxGXANe2TY0mSJKmeujsH+S7gfzZlw5m5DjiF4uwUdwP/lZl3RcRJEXHSpoUpSX3PmOZmIqIutzHNzY1+upI0aHR3BHk9sDgifknbOcgf6exBmXktxRkwqus6PCAvM4/vZiyS1Cc8tGwZK2fNqktbTXVqR5LU/QT5R+VNkiRJGtC6lSBn5rcjYkvg1Zl5b41jkiRJkhqmu1fSOxRYDPysXJ4QEXNrGJckSZLUEN09SG8WxZXxVgJk5mJg7MarS5IkSf1TdxPkdZn5dLt17S/6IUmSJPV73T1I786IOBYYEhG7Ah8BbqldWJIkSVJjdHcEeTqwO8Up3q4AVgEfrVFMkiRJUsN09ywW/0NxmekzahuOJEmS1FjdSpAjYhLwKWBM9TGZuVdtwpIkSZIao7tzkL8LnAbcAbxYu3AkSZKkxupugvxkZnreY0mSJA143T1I7zMRcXFEHBMR795wq2lkUg3MnDmTadOmMWPGjDbrzzrrLPbbbz/22Wcfrr766gZFJ0mS+oLuJsgnABOAg4FDy9s7axSTVBOLFi1i9erVzJs3jzVr1rBw4cLWslNPPZWbb76ZX/7yl5x99tkNjFKSJDVad6dYjM/MPWsaiVRj8+fPp6WlBYCWlhYWLFjAPvvsA8CwYcMAeO6559hjjz0aFqMkSWq87o4gL4iIcTWNRKqxlStXMmLECABGjhzJU0891ab85JNPZq+99uKggw5qRHiSJKmP6G6C/GZgcUTcGxG3R8QdEXF7LQOTeltTUxOrVq0CYNWqVTQ1NbUpv/DCC7nnnnv4whe+0IDoJElSX9HdBPlgYFfgbfxt/vGhtQpKqoWpU6dy4403AnDDDTcwZcqU1rIXXngBgC233LJ1lFmSJA1O3UqQM/Ohjm61Dk7qTRMnTmT48OFMmzaNzTbbjMmTJzN9+nQAZsyYwQEHHMABBxzAaaed1uBI+ybPACJJGiy6e5Ce6mxMczMPLVtWl7Z2Hj2aB5curUtbjXbuuee2WZ49ezYAc+bMaUQ4/Ub1DCAf+tCHWLhwYesBjqeeeiqf/OQnefbZZ2lpaeGII45ocLSSJL08Jsh91EPLlrFy1qy6tNVUp3bUf3kGEEnSYNLdOciSBjHPACJJGkxMkCV1yTOASJIGExNkSV3yDCCSpMHEBFlSlzwDiCRpMPEgPUnd4hlAJEmDhSPIkiRJUoUJsiRJklRhgixJkiRVmCBLkiRJFSbIkiRJUoUJsiRJklRhgixJkiRVmCBLkiRJFTVNkCPi4Ii4NyLuj4jTOyg/LCJuj4jFEXFrRLy5lvFIkiRJXanZlfQiYghwAfBWYCmwMCLmZuaSSrUbgbmZmRGxF/BfwG61ikmSJEnqSi1HkCcD92fmA5m5BrgSOKxaITOfzcwsF7cGEkmSJKmBajaCDIwGHqksLwX2bV8pIo4AzgJeAbyjow1FxInAiQDNzc0sX76814Pta8aNG8fKrbeuW1uDoU+l3ub7tGfst56x33rGfuuZevbbhvb6Ut/VMkGODta9ZIQ4M68Gro6I/YDPAS0d1LkIuAhg0qRJOWrUqF4Ote9ZsmQJTatX162twdCnUm/zfdoz9lvP2G89Y7/1TD37bUN7fanvajnFYimwU2W5GXh0Y5Uz82bgNRHRd3pHkiRJg04tE+SFwK4RMTYiNgeOBuZWK0TEayMiyvsTgc2BFTWMSZIkSepUzaZYZOa6iDgFuA4YAlySmXdFxEll+Rzgn4DjImIt8BxwVOWgPWmTjWlu5qFly+rS1s6jR/Pg0qV1aUuSJNVPLecgk5nXAte2Wzencv9s4OxaxqDB5aFly1g5a1Zd2mqqUzuSJKm+vJKeJEmSVGGCLEmSJFWYIEuSJEkVJsiSJElShQmyJMY0NxMRdbmNaW5u9NOVJKlTNT2LhaT+wbN/SJL0N44gS5IkSRUmyJIkSVKFCbIkSZJUYYIsSZIkVZggS5IkSRUmyJIkSVKFCbIkSZJUYYIsSZIkVZggS5IkSRUmyFI/NXPmTKZNm8aMGTParD/zzDOZOnUqU6dO5cYbb2xQdH2X/dYz9lvP2G+qN/e53mGCLPVDixYtYvXq1cybN481a9awcOHC1rLjjjuO+fPn89Of/pQzzzyzgVH2PfZbz9hvPWO/qd7c53qPCbLUD82fP5+WlhYAWlpaWLBgQWvZ2LFjAdhiiy2IiIbE11fZbz1jv/WM/aZ6c5/rPSbIUj+0cuVKRowYAcDIkSN56qmnXlJn1qxZfPCDH6x3aH2a/dYz9lvP2G+qN/e53mOCLPVDTU1NrFq1CoBVq1bR1NTUpvzqq69mxYoVHHvssQ2Iru+y33rGfusZ+0315j7Xe0yQpX6oepDFDTfcwJQpU1rLbr/9di644AIuuOCCRoXXZ9lvPWO/9Yz9pnpzn+s9JshSPzRx4kSGDx/OtGnT2GyzzZg8eTLTp08H4LTTTuPxxx/nH//xHznssMMaHGnfYr/1jP3WM/ab6s19rvcMbXQAknrm3HPPbbM8e/ZsAK677rpGhNNv2G89Y7/1jP2menOf6x2OIPcizz3YM/abJEnqS0yQe4nnHuwZ+02SJPU1Jsi9xHMP9oz9JkmS+hoT5F7iuQd7xn6TJEl9jQlyL/Hcgz1jv0mSpL7GBLmXeO7BnrHfJElSX2OC3Es892DP2G+SJKmv8TzIvchzD/aM/SZJkvoSR5AlSZKkChNkSZIkqaKmCXJEHBwR90bE/RFxegfl742I28vbLRExvpbxSJIkSV2pWYIcEUOAC4BDgHHAMRExrl21PwP7Z+ZewOeAi2oVjyRJktQdtRxBngzcn5kPZOYa4EqgzakIMvOWzNxwZYgFQHMN45EkSZK6VMuzWIwGHqksLwX27aT++4GfdlQQEScCJwI0NzezfPny3oqxzxo3bhwrt966bm0NlD6133rGfusZ+61n7Leesd96xn7rmXr224b2+lLf1TJBjg7WZYcVIw6kSJDf3FF5Zl5EOf1i0qRJOWrUqN6Ksc9asmQJTatX162tgdKn9lvP2G89Y7/1jP3WM/Zbz9hvPVPPftvQXl/qu1omyEuBnSrLzcCj7StFxF7AxcAhmbmihvFIkiRJXarlHOSFwK4RMTYiNgeOBuZWK0TEq4EfAv+amX+sYSySJElSt9RsBDkz10XEKcB1wBDgksy8KyJOKsvnAJ8GtgcujAiAdZk5qVYxSZIkSV2p6aWmM/Na4Np26+ZU7n8A+EAtY5AkSZI2hVfSkyRJkipMkCVJkqQKE2SpD2reeQwRUbfbQFLPvhtI7Leesd9UT+5v9VPTOciSembZww9x1qIn69beJyfuULe2aq2efWe/9Yz91jMDqd/UM+5v9eMIsiRJklRhgixJkiRVmCBLkiRJFSbIkiRJUoUJsiRJklRhgixJkiRVmCB3k+el7Rn7TZIk9TeeB7mbPC9tz9hvkiSpv3EEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZLU58ycOZNp06YxY8aMNusfffRRDjroIN74xjdyww03NCg6DXQ1TZAj4uCIuDci7o+I0zso3y0i5kfECxFxai1jkSRJ/cOiRYtYvXo18+bNY82aNSxcuLC17Itf/CKf//zn+fnPf87nP//5BkapgaxmCXJEDAEuAA4BxgHHRMS4dtX+CnwE+HKt4pAkSf3L/PnzaWlpAaClpYUFCxa0lt1+++1MnTqVbbbZhm233ZZnnnmmUWFqAKvlCPJk4P7MfCAz1wBXAodVK2TmE5m5EFhbwzgkSVI/snLlSkaMGAHAyJEjeeqpp1rL1q9fT0R0WCb1lqE13PZo4JHK8lJg355sKCJOBE4EaG5uZvny5S8/uk00btw4tnz+6bq2t3LrrevWVq361H7r+bbtt55vv159Z7/1vC37rWdtDZR+68rQoUNZunQpy5cvZ+nSpQwdOrQ1nhdffLH1/vLly1m/fn2nsQ6kfhuo+9uG9hq5z7VXywQ5OliXPdlQZl4EXAQwadKkHDVq1MuJq0eWLFnCc8NH1rW9ptWr69ZWrfrUfuv5tu23nm+/Xn1nv/W8LfutZ20NlH7rylvf+la+8Y1v8IEPfIDf/e53HH/88a3x7L333tx3333stddePP/884wdO7bTbQ2kfhuo+9uG9hq5z7VXyykWS4GdKsvNwKM1bE+SJA0AEydOZPjw4UybNo3NNtuMyZMnM336dAA+/vGPc8YZZ9DS0sKnPvWpBkeqgaqWI8gLgV0jYiywDDgaOLaG7UmSpAHi3HPPbbM8e/ZsoJhq+Ytf/KIRIWkQqVmCnJnrIuIU4DpgCHBJZt4VESeV5XMi4pXArcAI4MWI+CgwLjNX1SouSZIkqTO1HEEmM68Frm23bk7l/l8opl5IkiRJfYJX0pMkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIk1VXzzmOIiLrcpJ4Y2ugAJEnS4LLs4Yc4a9GTdWnrkxN3qEs7GlgcQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaowQZYkSZIqTJAlSZKkChNkSZIkqcIEWZIkSaqoaYIcEQdHxL0RcX9EnN5BeUTEeWX57RExsZbxSJIkSV2pWYIcEUOAC4BDgHHAMRExrl21Q4Bdy9uJwP+tVTySJElSd9RyBHkycH9mPpCZa4ArgcPa1TkMuDwLC4CmiNixhjFJkiRJnYrMrM2GI44EDs7MD5TL/wrsm5mnVOpcA3wxM39dLt8IfCIzb223rRMpRpgBXg/cW5Og+5ZRwPJGB9EP2W89Y7/1jP3WM/Zbz9hvPWO/9cxg6bedM3OH9iuH1rDB6GBd+2y8O3XIzIuAi3ojqP4iIm7NzEmNjqO/sd96xn7rGfutZ+y3nrHfesZ+65nB3m+1nGKxFNipstwMPNqDOpIkSVLd1DJBXgjsGhFjI2Jz4Ghgbrs6c4HjyrNZTAGezszHahiTJEmS1KmaTbHIzHURcQpwHTAEuCQz74qIk8ryOcC1wNuB+4H/AU6oVTz90KCaUtKL7Leesd96xn7rGfutZ+y3nrHfemZQ91vNDtKTJEmS+iOvpCdJkiRVmCBLkiRJFSbIfUxEXBIRT0TEnY2Opb+IiJ0i4pcRcXdE3BURMxodU38SEUMi4g/lecnVDRExs9zX7oyIKyJieKNj6qs29pkWEdMj4t6yH7/UqPj6oogYHhG/i4jbyv45s1x/TkTcExG3R8TVEdHU4FD7nIhoioiryn66OyKmVspOjYiMiFGNjLGv6Oi9ubF9LCKGRcS3I+KOsl8/2bDA68QEue+5DDi40UH0M+uAj2XmPwBTgA93cFlzbdwM4O5GB9FfRMRo4CPApMzcg+Ig5KMbG1WfdhntPtMi4kCKK6nulZm7A19uQFx92QvAQZk5HpgAHFye6el6YI/M3Av4IzDgk5QeOBf4WWbuBoyn/GyLiJ2AtwIPNzC2vuYyXppvbGwfew+wRWbuCewNfDAixtQpzoYwQe5jMvNm4K+NjqM/yczHMnNRef8Zig/E0Y2Nqn+IiGbgHcDFjY6lnxkKbBkRQ4Gt8PztG7WRz7QPUVxF9YWyzhN1D6wPy8Kz5eKw8paZ+fPMXFeuX0Bx7QCVImIEsB/wLYDMXJOZK8virwEfp4OLkQ1WHb03O9nHEti6/MzbElgDrKpXrI1ggqwBpfxG+wbgtw0Opb/4OsU/jRcbHEe/kZnLKEY8HwYeozh/+88bG1W/8zpgWkT8NiJ+FRH7NDqgvqac+rQYeAK4PjPbf6b9L+CndQ+sb9sFeBK4tJw2dnFEbB0R7wKWZeZtDY6vv6nuY1cBqyk+8x4GvpyZA3owzwRZA0ZEbAP8P+CjmTmgv9n2hoh4J/BEZv6+0bH0JxGxHcX0gLHAqyhGVf6lsVH1O0OB7SimRJ0G/FdERGND6lsyc31mTqAYwZscEXtsKIuIMyimln23QeH1VUOBicD/zcw3UCR0s4AzgE83MK5+p4N9bDKwnuIzbyzwsYjYpUHh1YUJsgaEiBhGkRx/NzN/2Oh4+ok3Ae+KiAeBK4GDIuI/GxtSv9AC/Dkzn8zMtcAPgTc2OKb+Zinww3Iqwe8ofsHwwKkOlFMEbqKcKxoR7wPeCbw3vZBBe0uBpZXR9qsoEuaxwG3lZ10zsCgiXtmYEPu+jexjx1LM7V5bTon6DTCpUTHWgwmy+r1y5OlbwN2Z+dVGx9NfZOYnM7M5M8dQHGT2i8x0JLRrDwNTImKrct97Cx7kuKl+BBwEEBGvAzYHljcyoL4kInaonD1gS4ovZfdExMHAJ4B3Zeb/NDDEPikz/wI8EhGvL1e9BViUma/IzDHlZ91SYGJZV+10so89TDGIEhGxNcWvP/c0IsZ6MUHuYyLiCmA+8PqIWBoR7290TP3Am4B/pXjzLi5vb290UBqYytGpq4BFwB0Un6OD+pKsndnIZ9olwC7l6aWuBN7naGgbOwK/jIjbgYUUc5CvAc4HtgWuLz/n5jQyyD5qOvDdsu8mAP/R2HD6ro28Nze2j10AbAPcSbFPXpqZtzci7nrxUtOSJElShSPIkiRJUoUJsiRJklRhgixJkiRVmCBLkiRJFSbIkiRJUoUJsiQ1QEScERF3RcTt5emU9q1xe7eUf8dExLGb+NgDIuKayvLnI+K6iNiit+OUpL5gaKMDkKTBJiKmUlypamJmvhARoygulvFytzs0M9d1VJaZG672N4biqljf62EbZ1Cce/ztmflCT7YhSX2dI8iSVH87Ass3JJiZuTwzHwWIiAcj4uyI+F15e225/tCI+G1E/CEiboiIvy/Xz4qIiyLi58DlEbF7+bjF5ej0rmW9Z8u2vwhMK8tnRsS8iJiwIbCI+E1E7NVR0BHxMeDtwKGZ+VxNekaS+gATZEmqv58DO0XEHyPiwojYv135qsycTHFVq6+X634NTMnMN1Bcfe7jlfp7A4dl5rHAScC5mTkBmERxad2q04F5mTkhM78GXAwcD62Xfd5iI1fIelO57UMy89kOyiVpwDBBlqQ6KxPMvYETgSeB70fE8ZUqV1T+Ti3vNwPXRcQdwGnA7pX6cysjuvOBT0XEJ4CduzHS+wPgnRExDPhfwGUbqXc/EMDbutieJPV7JsiS1ACZuT4zb8rMzwCnAP9ULe7g/mzg/MzcE/ggMLxSZ3Vlu98D3gU8R5FQH9RFHP8DXA8cBvwzG5+b/DjF9IqvRcSBXTw9SerXTJAlqc4i4vUb5gaXJgAPVZaPqvydX94fCSwr77+vk23vAjyQmecBc4H284mfAbZtt+5i4DxgYWb+dWPbzsw/Au8G/rM6b1mSBhoTZEmqv22Ab0fEkoi4HRgHzKqUbxERvwVmADPLdbOAH0TEPGB5J9s+CrgzIhYDuwGXtyu/HVgXEbdFxEyAzPw9sAq4tKvAM3MhcAIwNyJe01V9SeqPIjO7riVJqouIeBCYlJmdJcG93eargJuA3TLzxXq1K0l9lSPIkjSIRcRxwG+BM0yOJangCLIkSZJU4QiyJEmSVGGCLEmSJFWYIEuSJEkVJsiSJElShQmyJEmSVPH/ARysBp6Jn3ApAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "内存对比图已保存为 'fft_memory_comparison.png'\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tracemalloc\n",
    "\n",
    "# ==================== 传统FFT实现 ====================\n",
    "def traditional_fft(x):\n",
    "    \"\"\"标准迭代FFT（Cooley-Tukey）\"\"\"\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x\n",
    "\n",
    "    # 位逆序置换\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    # 迭代蝶形\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        for k in range(0, N, m):\n",
    "            w = 1.0\n",
    "            for j in range(m // 2):\n",
    "                t = w * x[k + j + m // 2]\n",
    "                u = x[k + j]\n",
    "                x[k + j] = u + t\n",
    "                x[k + j + m // 2] = u - t\n",
    "                w *= w_m\n",
    "    return x\n",
    "\n",
    "\n",
    "# ==================== GMT-FFT 实现（带剪枝） ====================\n",
    "def gmt_fft_sparse_with_trace(x, eps=1e-10):\n",
    "    \"\"\"GMT-FFT：路径剪枝 + 活跃集追踪\"\"\"\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x, [set(np.nonzero(np.abs(x) > eps)[0])]\n",
    "\n",
    "    # 位逆序置换\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    # 初始化活跃集\n",
    "    active_set = set(np.nonzero(np.abs(x) > eps)[0])\n",
    "    trace = [active_set.copy()]\n",
    "\n",
    "    # 迭代蝶形 + 剪枝\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        next_active = set()\n",
    "        for k in range(0, N, m):\n",
    "            for j in range(m // 2):\n",
    "                i1 = k + j\n",
    "                i2 = k + j + m // 2\n",
    "                # 剪枝：如果两个输入都不活跃，跳过\n",
    "                if i1 not in active_set and i2 not in active_set:\n",
    "                    continue\n",
    "                t = w_m**j * x[i2]\n",
    "                u = x[i1]\n",
    "                x[i1] = u + t\n",
    "                x[i2] = u - t\n",
    "                next_active.add(i1)\n",
    "                next_active.add(i2)\n",
    "        active_set = next_active\n",
    "        trace.append(active_set.copy())\n",
    "    return x, trace\n",
    "\n",
    "\n",
    "# ==================== 内存测量与绘图 ====================\n",
    "def main():\n",
    "    N = 1024\n",
    "    K_list = [1, 2, 4, 8, 16, 32, 64, 128]\n",
    "    mem_trad = []\n",
    "    mem_gmt = []\n",
    "\n",
    "    print(\"测量内存消耗中...\")\n",
    "    print(f\"{'K':<4} {'Trad (MB)':<12} {'GMT (MB)':<12} {'Diff (MB)':<12}\")\n",
    "\n",
    "    for K in K_list:\n",
    "        # 生成稀疏信号\n",
    "        x = np.zeros(N)\n",
    "        idx = np.random.choice(N, K, replace=False)\n",
    "        x[idx] = np.random.randn(K) + 1j * np.random.randn(K)\n",
    "\n",
    "        # 测量传统FFT\n",
    "        tracemalloc.start()\n",
    "        _ = traditional_fft(x)\n",
    "        _, peak_trad = tracemalloc.get_traced_memory()\n",
    "        tracemalloc.stop()\n",
    "\n",
    "        # 测量GMT-FFT\n",
    "        tracemalloc.start()\n",
    "        _, _ = gmt_fft_sparse_with_trace(x)\n",
    "        _, peak_gmt = tracemalloc.get_traced_memory()\n",
    "        tracemalloc.stop()\n",
    "\n",
    "        # 转换为MB\n",
    "        mb_trad = peak_trad / 1024 ** 2\n",
    "        mb_gmt = peak_gmt / 1024 ** 2\n",
    "        mem_trad.append(mb_trad)\n",
    "        mem_gmt.append(mb_gmt)\n",
    "\n",
    "        print(f\"{K:<4} {mb_trad:<12.2f} {mb_gmt:<12.2f} {mb_gmt - mb_trad:<12.2f}\")\n",
    "\n",
    "    # 绘图\n",
    "    x_pos = np.arange(len(K_list))\n",
    "    width = 0.35\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 6))\n",
    "    bar1 = ax.bar(x_pos - width/2, mem_trad, width, label='traditional FFT', color='skyblue', edgecolor='black')\n",
    "    bar2 = ax.bar(x_pos + width/2, mem_gmt, width, label='GMT-FFT', color='lightcoral', edgecolor='black')\n",
    "\n",
    "    ax.set_xlabel('Sparsity K')\n",
    "    ax.set_ylabel('mem use (MB)')\n",
    "    ax.set_title('GMT-FFT vs traditional FFT：Memory Consumption Comparison')\n",
    "    ax.set_xticks(x_pos)\n",
    "    ax.set_xticklabels(K_list)\n",
    "    ax.legend()\n",
    "    ax.grid(True, axis='y', alpha=0.3)\n",
    "\n",
    "    # 在柱子上方标注数值\n",
    "    for i, (t, g) in enumerate(zip(mem_trad, mem_gmt)):\n",
    "        ax.text(i - width/2, t + 0.05, f'{t:.1f}', ha='center', va='bottom', fontsize=8)\n",
    "        ax.text(i + width/2, g + 0.05, f'{g:.1f}', ha='center', va='bottom', fontsize=8)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('fft_memory_comparison.png', dpi=300)\n",
    "    plt.show()\n",
    "\n",
    "    print(\"内存对比图已保存为 'fft_memory_comparison.png'\")\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "测试补零情况下，GMT-FFT的优势"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "理论上来说补零越多，GMT-FFT的计算速度优势越明显"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K    Trad FFT (ms)  GMT-FFT (ms)   Speedup  Zero Ratio (%)\n",
      "------------------------------------------------------------\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-8-15bf64a6a698>:9: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[non_zero_indices] = np.random.randn(len(non_zero_indices)) + 1j * np.random.randn(len(non_zero_indices))\n",
      "<ipython-input-8-15bf64a6a698>:39: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[k + j] = u + t\n",
      "<ipython-input-8-15bf64a6a698>:40: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[k + j + m // 2] = u - t\n",
      "<ipython-input-8-15bf64a6a698>:79: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[i1] = u + t\n",
      "<ipython-input-8-15bf64a6a698>:80: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  x[i2] = u - t\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64   208.863        100.111        2.09     98.4          \n",
      "128  197.591        117.491        1.68     96.9          \n",
      "256  199.336        125.375        1.59     93.8          \n",
      "512  195.480        146.926        1.33     87.5          \n",
      "1024 192.239        166.862        1.15     75.0          \n",
      "2048 195.439        186.342        1.05     50.0          \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "最大加速比：2.09x（当 K=64）\n",
      "图表已保存为 'fft_padded_comparison.png'\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "# 生成稀疏信号\n",
    "def generate_sparse_signal(K, sparsity=0.1):\n",
    "    x = np.zeros(K)\n",
    "    non_zero_indices = np.random.choice(K, int(K * sparsity), replace=False)\n",
    "    x[non_zero_indices] = np.random.randn(len(non_zero_indices)) + 1j * np.random.randn(len(non_zero_indices))\n",
    "    return x\n",
    "\n",
    "# 传统FFT实现（Cooley-Tukey 迭代版）\n",
    "def traditional_fft(x):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x\n",
    "\n",
    "    # 位逆序置换\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    # 迭代蝶形\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        for k in range(0, N, m):\n",
    "            w = 1.0\n",
    "            for j in range(m // 2):\n",
    "                t = w * x[k + j + m // 2]\n",
    "                u = x[k + j]\n",
    "                x[k + j] = u + t\n",
    "                x[k + j + m // 2] = u - t\n",
    "                w *= w_m\n",
    "    return x\n",
    "\n",
    "# GMT-FFT 实现（带剪枝）\n",
    "def gmt_fft_sparse_with_trace(x, eps=1e-10):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x, [set(np.nonzero(np.abs(x) > eps)[0])]\n",
    "\n",
    "    # 位逆序置换\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    # 初始化活跃集\n",
    "    active_set = set(np.nonzero(np.abs(x) > eps)[0])\n",
    "    trace = [active_set.copy()]\n",
    "\n",
    "    # 迭代蝶形 + 剪枝\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        next_active = set()\n",
    "        for k in range(0, N, m):\n",
    "            for j in range(m // 2):\n",
    "                i1 = k + j\n",
    "                i2 = k + j + m // 2\n",
    "                if i1 not in active_set and i2 not in active_set:\n",
    "                    continue  # 剪枝\n",
    "                t = w_m**j * x[i2]\n",
    "                u = x[i1]\n",
    "                x[i1] = u + t\n",
    "                x[i2] = u - t\n",
    "                next_active.add(i1)\n",
    "                next_active.add(i2)\n",
    "        active_set = next_active\n",
    "        trace.append(active_set.copy())\n",
    "    return x, trace\n",
    "\n",
    "# 性能对比实验\n",
    "def main():\n",
    "    N_target = 4096  # 补到的目标长度\n",
    "    K_list = [64, 128, 256, 512, 1024, 2048]  # 原始信号长度（其余补零）\n",
    "    num_runs = 50  # 每次运行次数（取平均）\n",
    "\n",
    "    times_trad = []\n",
    "    times_gmt = []\n",
    "    speedups = []\n",
    "\n",
    "    print(f\"{'K':<4} {'Trad FFT (ms)':<14} {'GMT-FFT (ms)':<14} {'Speedup':<8} {'Zero Ratio (%)':<14}\")\n",
    "    print(\"-\" * 60)\n",
    "\n",
    "    for K in K_list:\n",
    "        # 生成稀疏信号\n",
    "        x_orig = generate_sparse_signal(K, sparsity=0.1)\n",
    "        x_padded = np.pad(x_orig, (0, N_target - K), mode='constant')  # 补零到4096\n",
    "\n",
    "        # 测量传统FFT\n",
    "        times = []\n",
    "        for _ in range(num_runs):\n",
    "            start = time.perf_counter()\n",
    "            _ = traditional_fft(x_padded)\n",
    "            times.append(time.perf_counter() - start)\n",
    "        time_trad = np.mean(times) * 1000  # ms\n",
    "\n",
    "        # 测量GMT-FFT\n",
    "        times = []\n",
    "        for _ in range(num_runs):\n",
    "            start = time.perf_counter()\n",
    "            _, _ = gmt_fft_sparse_with_trace(x_padded)\n",
    "            times.append(time.perf_counter() - start)\n",
    "        time_gmt = np.mean(times) * 1000  # ms\n",
    "\n",
    "        speedup = time_trad / time_gmt\n",
    "        zero_ratio = (N_target - K) / N_target * 100  # 百分比\n",
    "\n",
    "        times_trad.append(time_trad)\n",
    "        times_gmt.append(time_gmt)\n",
    "        speedups.append(speedup)\n",
    "\n",
    "        print(f\"{K:<4} {time_trad:<14.3f} {time_gmt:<14.3f} {speedup:<8.2f} {zero_ratio:<14.1f}\")\n",
    "\n",
    "    # 绘图\n",
    "    x_pos = np.arange(len(K_list))\n",
    "    width = 0.35\n",
    "\n",
    "    fig, ax1 = plt.subplots(figsize=(10, 6))\n",
    "\n",
    "    # 柱状图：时间对比\n",
    "    bar1 = ax1.bar(x_pos - width/2, times_trad, width, label='traditional FFT', color='skyblue', edgecolor='black')\n",
    "    bar2 = ax1.bar(x_pos + width/2, times_gmt, width, label='GMT-FFT', color='lightcoral', edgecolor='black')\n",
    "\n",
    "    ax1.set_xlabel('Original Signal Length K')\n",
    "    ax1.set_ylabel('Average Execution Time (ms)', color='black')\n",
    "    ax1.set_title(f'Zero-Padding to {N_target}: Execution Time Comparison Between Traditional FFT and GMT-FFT')\n",
    "    ax1.set_xticks(x_pos)\n",
    "    ax1.set_xticklabels(K_list)\n",
    "    ax1.legend(loc='upper left')\n",
    "    ax1.grid(True, axis='y', alpha=0.3)\n",
    "\n",
    "    # 折线图：加速比（右侧y轴）\n",
    "    ax2 = ax1.twinx()\n",
    "    line = ax2.plot(x_pos, speedups, 'o-', color='darkgreen', linewidth=2, label='Speedup Ratio')\n",
    "    ax2.set_ylabel('Speedup Ratio (x)', color='darkgreen')\n",
    "    ax2.tick_params(axis='y', labelcolor='darkgreen')\n",
    "\n",
    "    # 合并图例\n",
    "    lines, labels = ax1.get_legend_handles_labels()\n",
    "    lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "    ax1.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('fft_padded_comparison.png', dpi=300)\n",
    "    plt.show()\n",
    "\n",
    "    print(f\"\\n最大加速比：{max(speedups):.2f}x（当 K={K_list[np.argmax(speedups)]}）\")\n",
    "    print(\"图表已保存为 'fft_padded_comparison.png'\")\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "下面需要在真实数据进行实验，"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GMT-FFT只在稀疏情况下表现良好，上面的数据不够稀疏所以这样的表现很正常，说明GMT-FFT只适用于稀疏信号，下面用稀疏的真实数据实验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Signal 'spikes': non-zero ratio = 1.17%\n",
      "Zero-padding ratio = 50.0%\n",
      "Traditional FFT: 23.104 ms\n",
      "GMT-FFT: 13.091 ms\n",
      "✅ Speedup: 1.76x\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "# ========== 手动定义 spikes 信号（复现 pywt.data.spikes 的原始行为）==========\n",
    "def spikes(n=1024):\n",
    "    \"\"\"\n",
    "    Generate a synthetic 'spikes' signal: a series of impulses at specific locations.\n",
    "    This mimics the original pywt.data.spikes() from older versions.\n",
    "    \"\"\"\n",
    "    x = np.zeros(n)\n",
    "    indices = [0, 50, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]\n",
    "    values = [1.0, 0.8, 0.9, 0.7, 0.8, 0.6, 0.7, 0.5, 0.6, 0.4, 0.5, 0.3]\n",
    "    for i, v in zip(indices, values):\n",
    "        if i < n:\n",
    "            x[i] = v\n",
    "    return x\n",
    "\n",
    "# ========== 传统FFT实现（Cooley-Tukey 迭代版）==========\n",
    "def traditional_fft(x):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x\n",
    "\n",
    "    # 位逆序置换\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    # 迭代蝶形\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        for k in range(0, N, m):\n",
    "            w = 1.0\n",
    "            for j in range(m // 2):\n",
    "                t = w * x[k + j + m // 2]\n",
    "                u = x[k + j]\n",
    "                x[k + j] = u + t\n",
    "                x[k + j + m // 2] = u - t\n",
    "                w *= w_m\n",
    "    return x\n",
    "\n",
    "# ========== GMT-FFT 实现（带剪枝）==========\n",
    "def gmt_fft_sparse_with_trace(x, eps=1e-3):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x, [set(np.nonzero(np.abs(x) > eps)[0])]\n",
    "\n",
    "    # 位逆序置换\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    # 初始化活跃集\n",
    "    active_set = set(np.nonzero(np.abs(x) > eps)[0])\n",
    "    trace = [active_set.copy()]\n",
    "\n",
    "    # 迭代蝶形 + 剪枝\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        next_active = set()\n",
    "        for k in range(0, N, m):\n",
    "            for j in range(m // 2):\n",
    "                i1 = k + j\n",
    "                i2 = k + j + m // 2\n",
    "                if i1 not in active_set and i2 not in active_set:\n",
    "                    continue  # 剪枝\n",
    "                t = w_m**j * x[i2]\n",
    "                u = x[i1]\n",
    "                x[i1] = u + t\n",
    "                x[i2] = u - t\n",
    "                next_active.add(i1)\n",
    "                next_active.add(i2)\n",
    "        active_set = next_active\n",
    "        trace.append(active_set.copy())\n",
    "    return x, trace\n",
    "\n",
    "# ========== 主实验：使用重建的 spikes 信号 ==========\n",
    "def main_spikes_experiment():\n",
    "    N_target = 2048  # 补零到 2048 = 2^11\n",
    "    num_runs = 50     # 每次运行次数\n",
    "\n",
    "    # 生成极度稀疏的真实风格信号\n",
    "    x_orig = spikes(n=1024)  # 1024点，只有12个非零点！\n",
    "    x_orig = x_orig.astype(complex)\n",
    "    x_padded = np.pad(x_orig, (0, N_target - len(x_orig)), mode='constant')  # 补零\n",
    "\n",
    "    # 统计稀疏性\n",
    "    non_zero_ratio = np.count_nonzero(x_orig) / len(x_orig) * 100\n",
    "    zero_ratio = (N_target - len(x_orig)) / N_target * 100\n",
    "    print(f\"Signal 'spikes': non-zero ratio = {non_zero_ratio:.2f}%\")\n",
    "    print(f\"Zero-padding ratio = {zero_ratio:.1f}%\")\n",
    "\n",
    "    # 测量传统FFT\n",
    "    times = []\n",
    "    for _ in range(num_runs):\n",
    "        start = time.perf_counter()\n",
    "        _ = traditional_fft(x_padded)\n",
    "        times.append(time.perf_counter() - start)\n",
    "    t_trad = np.mean(times) * 1000  # ms\n",
    "\n",
    "    # 测量GMT-FFT\n",
    "    times = []\n",
    "    for _ in range(num_runs):\n",
    "        start = time.perf_counter()\n",
    "        _, _ = gmt_fft_sparse_with_trace(x_padded, eps=1e-3)\n",
    "        times.append(time.perf_counter() - start)\n",
    "    t_gmt = np.mean(times) * 1000  # ms\n",
    "\n",
    "    speedup = t_trad / t_gmt\n",
    "\n",
    "    print(f\"Traditional FFT: {t_trad:.3f} ms\")\n",
    "    print(f\"GMT-FFT: {t_gmt:.3f} ms\")\n",
    "    print(f\"✅ Speedup: {speedup:.2f}x\")\n",
    "\n",
    "    # 可视化信号\n",
    "    plt.figure(figsize=(12, 4))\n",
    "    plt.plot(x_padded.real, label='Spikes Signal (zero-padded to 2048)', color='black', linewidth=1.2)\n",
    "    plt.xlabel('Sample Index', fontsize=12)\n",
    "    plt.ylabel('Amplitude', fontsize=12)\n",
    "    plt.title('Synthetic Sparse Signal: \"spikes\" (reconstructed, zero-padded to 2048)', fontsize=14)\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('spikes_signal_reconstructed.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "    return speedup\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main_spikes_experiment()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ECG Signal: non-zero ratio = 5.37% (稀疏化后)\n",
      "Traditional FFT: 24.157 ms\n",
      "GMT-FFT: 22.205 ms\n",
      "✅ Speedup: 1.09x\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import pywt  # 确保已安装: pip install PyWavelets\n",
    "\n",
    "# 传统FFT实现\n",
    "def traditional_fft(x):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        for k in range(0, N, m):\n",
    "            w = 1.0\n",
    "            for j in range(m // 2):\n",
    "                t = w * x[k + j + m // 2]\n",
    "                u = x[k + j]\n",
    "                x[k + j] = u + t\n",
    "                x[k + j + m // 2] = u - t\n",
    "                w *= w_m\n",
    "    return x\n",
    "\n",
    "# GMT-FFT实现\n",
    "def gmt_fft_sparse_with_trace(x, eps=1e-5):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x, [set(np.nonzero(np.abs(x) > eps)[0])]\n",
    "\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    active_set = set(np.nonzero(np.abs(x) > eps)[0])\n",
    "    trace = [active_set.copy()]\n",
    "\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        next_active = set()\n",
    "        for k in range(0, N, m):\n",
    "            for j in range(m // 2):\n",
    "                i1 = k + j\n",
    "                i2 = k + j + m // 2\n",
    "                if i1 not in active_set and i2 not in active_set:\n",
    "                    continue\n",
    "                t = w_m**j * x[i2]\n",
    "                u = x[i1]\n",
    "                x[i1] = u + t\n",
    "                x[i2] = u - t\n",
    "                next_active.add(i1)\n",
    "                next_active.add(i2)\n",
    "        active_set = next_active\n",
    "        trace.append(active_set.copy())\n",
    "    return x, trace\n",
    "\n",
    "# 主实验：使用真实ECG信号\n",
    "def main_ecg_experiment():\n",
    "    N_target = 2048  # 补零到2048\n",
    "    num_runs = 50\n",
    "\n",
    "    # 加载PyWavelets中的真实ECG信号（大多数版本都包含这个信号）\n",
    "    x_orig = pywt.data.ecg()  # 真实的心电图信号\n",
    "    x_orig = x_orig.astype(complex)\n",
    "    \n",
    "    # 对信号进行稀疏化处理（保留显著峰值，模拟稀疏特性）\n",
    "    threshold = np.percentile(np.abs(x_orig), 95)  # 取95%分位值作为阈值\n",
    "    x_sparse = x_orig.copy()\n",
    "    x_sparse[np.abs(x_sparse) < threshold] = 0  # 过滤掉小幅度值，增强稀疏性\n",
    "    \n",
    "    # 补零到目标长度\n",
    "    x_padded = np.pad(x_sparse, (0, max(0, N_target - len(x_sparse))), 'constant')\n",
    "\n",
    "    # 计算稀疏度\n",
    "    non_zero_ratio = np.count_nonzero(x_sparse) / len(x_sparse) * 100\n",
    "    print(f\"ECG Signal: non-zero ratio = {non_zero_ratio:.2f}% (稀疏化后)\")\n",
    "\n",
    "    # 测试传统FFT\n",
    "    times = []\n",
    "    for _ in range(num_runs):\n",
    "        start = time.perf_counter()\n",
    "        _ = traditional_fft(x_padded)\n",
    "        times.append(time.perf_counter() - start)\n",
    "    t_trad = np.mean(times) * 1000\n",
    "\n",
    "    # 测试GMT-FFT\n",
    "    times = []\n",
    "    for _ in range(num_runs):\n",
    "        start = time.perf_counter()\n",
    "        _, _ = gmt_fft_sparse_with_trace(x_padded, eps=1e-3)\n",
    "        times.append(time.perf_counter() - start)\n",
    "    t_gmt = np.mean(times) * 1000\n",
    "\n",
    "    speedup = t_trad / t_gmt\n",
    "\n",
    "    print(f\"Traditional FFT: {t_trad:.3f} ms\")\n",
    "    print(f\"GMT-FFT: {t_gmt:.3f} ms\")\n",
    "    print(f\"✅ Speedup: {speedup:.2f}x\")\n",
    "\n",
    "    # 可视化信号\n",
    "    plt.figure(figsize=(12, 4))\n",
    "    plt.plot(x_padded.real, label='ECG Signal (sparsified + zero-padded)', color='black')\n",
    "    plt.xlabel('Sample Index')\n",
    "    plt.ylabel('Amplitude')\n",
    "    plt.title('Real ECG Signal (sparsified and zero-padded to 2048)')\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('ecg_signal.png', dpi=300)\n",
    "    plt.show()\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main_ecg_experiment()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-99f1da6d0d21>:81: DeprecationWarning: scipy.misc.electrocardiogram has been deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. Dataset methods have moved into the scipy.datasets module. Use scipy.datasets.electrocardiogram instead.\n",
      "  ecg_signal = electrocardiogram()  # 真实医学信号\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Real Sparse Signal: non-zero ratio = 1.00% (高稀疏处理后)\n",
      "Traditional FFT: 23.793 ms\n",
      "GMT-FFT: 17.307 ms\n",
      "✅ Speedup: 1.37x\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import scipy  # 确保已安装: pip install scipy\n",
    "from scipy.misc import electrocardiogram  # 真实心电图信号\n",
    "\n",
    "# 传统FFT实现\n",
    "def traditional_fft(x):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        for k in range(0, N, m):\n",
    "            w = 1.0\n",
    "            for j in range(m // 2):\n",
    "                t = w * x[k + j + m // 2]\n",
    "                u = x[k + j]\n",
    "                x[k + j] = u + t\n",
    "                x[k + j + m // 2] = u - t\n",
    "                w *= w_m\n",
    "    return x\n",
    "\n",
    "# GMT-FFT实现\n",
    "def gmt_fft_sparse_with_trace(x, eps=1e-5):\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N <= 1:\n",
    "        return x, [set(np.nonzero(np.abs(x) > eps)[0])]\n",
    "\n",
    "    num_bits = N.bit_length() - 1\n",
    "    rev = np.arange(N)\n",
    "    rev = (((rev & 0xaaaaaaaa) >> 1) | ((rev & 0x55555555) << 1)) & 0xffffffff\n",
    "    rev = (((rev & 0xcccccccc) >> 2) | ((rev & 0x33333333) << 2)) & 0xffffffff\n",
    "    rev = (((rev & 0xf0f0f0f0) >> 4) | ((rev & 0x0f0f0f0f) << 4)) & 0xffffffff\n",
    "    rev = (((rev & 0xff00ff00) >> 8) | ((rev & 0x00ff00ff) << 8)) & 0xffffffff\n",
    "    rev = (rev >> 16) | (rev << 16)\n",
    "    rev >>= (32 - num_bits)\n",
    "    x = x[rev]\n",
    "\n",
    "    active_set = set(np.nonzero(np.abs(x) > eps)[0])\n",
    "    trace = [active_set.copy()]\n",
    "\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        next_active = set()\n",
    "        for k in range(0, N, m):\n",
    "            for j in range(m // 2):\n",
    "                i1 = k + j\n",
    "                i2 = k + j + m // 2\n",
    "                if i1 not in active_set and i2 not in active_set:\n",
    "                    continue\n",
    "                t = w_m**j * x[i2]\n",
    "                u = x[i1]\n",
    "                x[i1] = u + t\n",
    "                x[i2] = u - t\n",
    "                next_active.add(i1)\n",
    "                next_active.add(i2)\n",
    "        active_set = next_active\n",
    "        trace.append(active_set.copy())\n",
    "    return x, trace\n",
    "\n",
    "# 主实验：使用高稀疏真实信号\n",
    "def main_sparse_real_experiment():\n",
    "    N_target = 2048  # 补零到2048\n",
    "    num_runs = 50\n",
    "\n",
    "    # 加载scipy中的真实心电图信号（高稀疏性潜力）\n",
    "    ecg_signal = electrocardiogram()  # 真实医学信号\n",
    "    x_orig = ecg_signal[:1000]  # 取前1000个点（缩短信号增强稀疏处理效果）\n",
    "    x_orig = x_orig.astype(complex)\n",
    "    \n",
    "    # 高强度稀疏化处理（只保留1%的显著峰值）\n",
    "    threshold = np.percentile(np.abs(x_orig), 99)  # 99%分位值作为阈值\n",
    "    x_sparse = x_orig.copy()\n",
    "    x_sparse[np.abs(x_sparse) < threshold] = 0  # 只保留最强的1%信号\n",
    "    \n",
    "    # 补零到目标长度\n",
    "    x_padded = np.pad(x_sparse, (0, max(0, N_target - len(x_sparse))), 'constant')\n",
    "\n",
    "    # 计算稀疏度（非零元素比例）\n",
    "    non_zero_ratio = np.count_nonzero(x_sparse) / len(x_sparse) * 100\n",
    "    print(f\"Real Sparse Signal: non-zero ratio = {non_zero_ratio:.2f}% (高稀疏处理后)\")\n",
    "\n",
    "    # 测试传统FFT\n",
    "    times = []\n",
    "    for _ in range(num_runs):\n",
    "        start = time.perf_counter()\n",
    "        _ = traditional_fft(x_padded)\n",
    "        times.append(time.perf_counter() - start)\n",
    "    t_trad = np.mean(times) * 1000\n",
    "\n",
    "    # 测试GMT-FFT\n",
    "    times = []\n",
    "    for _ in range(num_runs):\n",
    "        start = time.perf_counter()\n",
    "        _, _ = gmt_fft_sparse_with_trace(x_padded, eps=1e-3)\n",
    "        times.append(time.perf_counter() - start)\n",
    "    t_gmt = np.mean(times) * 1000\n",
    "\n",
    "    speedup = t_trad / t_gmt\n",
    "\n",
    "    print(f\"Traditional FFT: {t_trad:.3f} ms\")\n",
    "    print(f\"GMT-FFT: {t_gmt:.3f} ms\")\n",
    "    print(f\"✅ Speedup: {speedup:.2f}x\")\n",
    "\n",
    "    # 可视化信号（突出稀疏特性）\n",
    "    plt.figure(figsize=(12, 4))\n",
    "    plt.plot(x_padded.real, label='Highly Sparse Real Signal', color='black')\n",
    "    plt.scatter(np.where(x_padded.real != 0)[0], x_padded.real[np.where(x_padded.real != 0)], \n",
    "                color='red', zorder=5, label='Non-zero Elements')\n",
    "    plt.xlabel('Sample Index')\n",
    "    plt.ylabel('Amplitude')\n",
    "    plt.title('Highly Sparse Real ECG Signal (zero-padded to 2048)')\n",
    "    plt.legend()\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('highly_sparse_signal.png', dpi=300)\n",
    "    plt.show()\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main_sparse_real_experiment()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13.3\n"
     ]
    }
   ],
   "source": [
    "import neo\n",
    "print(neo.__version__)  # 打印版本号，若输出 0.13.3 则确认无误"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Signal Length: 8192\n",
      "Non-zero ratio: 0.0610%\n",
      "Naive FFT  FLOPs: 532,480\n",
      "GMT-FFT    FLOPs: 104,418\n",
      "FLOPs Speedup: 5.10x\n",
      "Max error: 0.00e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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3VscexExVLaZ7SOMek3k/JEnLVlWXVNVngAvGL2vf8X8B/GNV3VlVP6K7+fmSntVeCCzsuQEK8BG6B85PpzcAdwIHVdWvquruqjoOeB/wrxNdI9uDhf8HeGSSdZN8vtV+3ZrkrCRbTXSgdK1X3pLkPOCuds3fI8mP27b/l2TPnvV3bNexO5IspEv+xpY9oJVHelrHJFkjydt6fqOcnWS7JD9sq/9fu7a+cPy+kvxhutrKW5NckOS5Pcs+2347fLPt94wkD1vJ91yrAROs4fcooLcZwiLgoiTPbV8gz6N7kvh5k9hX2jS+7JHLWP9pTHBx6PFz4Kl0NV/vBj6fZGuAJC+geyL8S+lq2p4L3FRVL6F7Gvtz2t21D47b50nAw5Ps3FP2IroaFoAPAH8APBrYCdgWeOdyYhzv2cDjgd2AvwT2nuR236IblnVL4BzgCz3LPgO8sqo2pHsvv1dVd9Elx9f03Em8ZoL9rsy299FdDOcCT6S7i/hqgCRzgROBtwKb031mnjR2kPY5eRtdMr0F3cXxuHGxXNTeF0nSxP45XbO//+1NBlbSHwD3VdXPesr+j64GCYCq+le67+lvJ9kwyfuBP6YbKnw6PRP4clX9blz5CXQ3Q/9g/AZJdqG79v8EOJDuN8B2dNeeQ4C7l3O8A4A/pWtFsxXwTbqWM5sBbwS+nPtr7o4Fzqa75r23HWuy/r4daz+63yCvAH5dVU9ry3dr19Yvjju3tYCvA9+hu96/DvhCkt7aygPofvNsClxGl4xqxJhgDb9NgDvGZlo/pWPovnh+0/6+sv0oX5Ef09WKHJBkrSQH0tV8PWj8ikmeSfdltszkpdWEXVNVv2tfUpcCu7fFfw18sKrOajVtl1XVL1YUYFX9Gvga3RcYLdF6BHBSu5P2N8AbqurmqroD+CdgwSTOfcz7q+rWqroK+D5dorZCVXVUVd3R+iu9C9gtycZt8W+BXZJsVFW3VNU5KxHPpLetqrOr6vSqWlJVV9L1y/vjtng/4IKq+kpVLQEOB37Vs/krgX+uqova8n8CHt1bi0X3OdtkJWKXpFHyFuChdDf2jqRribEqtRcbALeNK7sNGN/n+W+BC+ludO4PPLO1LlmePVrNy9i0olYJc4FrJyi/tmf5mHOS3EKXgHwa+E+6a9jmwE6tZczZVXX7co53eFVd3bo9/BVdF4iT2++IhXQ3kfdLsj3dzdB/rKrfVNUP23En66+Bd7SaxKqq/6uqmyax3R50/z7vr6p7q+p7wDdov0mar7TWQkvobrY+eiXi0mrCBGv43ULPl26r/v4gsCewNt0P7E8nefSKdtS+XPanu7NzHbAP8N/A+Gr2PegSt+ePu8PGuPVemuTcsS9yuhqYsS/j7ehquFbFsdz/ZfYi4L9a4rUFXTJ4ds8xv93KJ6s36fg13RfpcrWawve3pga3c/+T28fO9S/oEpxftOYMT1yJeCa9bZI/SPKNdE0Vb6dLksZi2Aa4emzd9vDD3n/XhwAf7Xnfbqarvdy2Z50NgVtXInZJGhlVdcbYjbaqOhr4X7rv75V1J12tSq+N6LmZ2o5XdC0LtqD7Pl9e4jLm9KrapGc6fQXr3whsPUH51j3Lxzy2qjatqodV1TtardfngFOA45Nck+SDrRZoWa7uef0Q4AW9CSHwlHbsbYBbxt08XuFN2h6r+htkG+DqcTV6v2Dpa+VK/47Q6scEa/idx9JV9I8GflhVi9odn7OAM4BnTLTxeFX1g6p6fFVtRtfe++HAmWPL03WgPQl4RVV9d1n7aTUf/wG8Fti8qjYBzuf+JohX0/qFTRTGCsL8DjC3JY0HcH/zwBvpmh7s2nPx2Li6Trcz6UV0iekz6JpC7NDKA9Bq6fana07wX3RNK2DF57my234SuBjYuao2omvyN/Z+X0vXP68LrKvtm9ez7dV0NZ29F971qurHPev8IV0zFUnSihUPbHY/GT8D1hzXFH43xjXJT/Jq4FXALnQ3v760guRlVfw38BdJxv9e/Eu668Yyb7ICVNVvq+rdVbULXbP0Z9N1DVjmJj2vrwY+N+66tH5VvZ/umrZpuv5qY7bveX0XPa1v0o1o2HuzdXm/QZbnGmC7ce/H9sAvV2FfWo2ZYA2/k7m/GRjAWcBTx2qsWkL0VFofrCRzkqwLrNXNZt0sPRDCY1rzwI2ADwGLq+qUtuyRdDVCr6uqFVXFr0/3RXlD2/blLN2X69PAG5M8Lp2depqjXUfXzGJCrdr9RLoRDDcDFrby39Eldf+WNmpikm2TTLYf1arakK455k10X+j/NLYgydrpnre1cVX9lu4O49hw89cBm/c0JVzKKmy7YVvnziSPoLvwjvkm8Kgkz0s3OtNrgAf3LD8CeGva4BxJNm795MZi2ZbuvV7R3U5JmnFJ9kk3aM9lSQ6dYPme6Qb0ObdN7+xZVukGVBqbXzPJDUm+MYV4Nkmyd7umrpnkxXT9lE9Zxvpp1+K12/y6aaO0tlqZrwDvSbJ+kifT3cTrjfkldH1qn1FVV9Dd6AtL9/9dWWu0OMamtelGDNwI+EySB7fyA4C3A29qtWjLe1+enuRRLcG5na7J4GQfufJ54DntfR2Lbc8k81qXgkXAu9u18inAc3q2/RmwbrrHy6wFvAPoHQX308B7k+zc/i3+KMnmbdnyfoOcQZe8vbn9VtqzHff4SZ6TRoQJ1vA7hq498nrQ1UDR9QE6MckdwJeBf6qqsQfqPo2uludkursud9PVCI15M11N0NV01fC9I//9A90doM/k/tHrJhzkoqouBP4VOI3uy+pRdM0lxpZ/ia7j57F0zR7+i+4HPMA/A+9oTQLeuIzzPpauxuhLLeEa8xa6TqWnt2Zy/01XCzeTjqFrIvBLuvbw45OQlwBXtngOoWtXPjbS0nHA5e1cHzCK4Epu+0a6i+wddInm7zvnVtWNwAvomo/eRHfHcxFdYkhVfZVugJDj27HOpxtIY8yLgKNbHzNJ6pv2Y/3jdN9RuwAHpBtYYbz/qapHt+k9PeV30Y1wNzbC7DOZeg3EWnSDMdxAdw19HfC8qrqkxbx9u2aO1bI8hO76O3YNvZulB6x6NbAecD3dd/2rqqr3ensBXZ+rn0NXUwQ8n57v/VVwaItjbPpe6zrwFGBduuvbTXTdCF5S4waAWIYH090QvZ2uOeMP6BKnFaqqq+kSy7fRva9X0z1iZuy364uAJ9A1aT+M7lo8tu1tdO/hp+n+be9i6WbxH6ZrEfKdFttn6N5v6H5DHd2urX85LqZ76Qbl2pfu3/kTwEvbNVn6vazg5oOGQJJ/Aq6vqo/0OxYNh9a8YTHw4qr6/grWXYeuaeDTqur62YhPkpYlXV/Ud1XV3m3+rQBV9c896+wJvLGqnj3B9nfSDfRzTlWdmOQYuoTlqROtL0kryxqs1UBVvc3kSivSmlls0hKmsf5ZK2zy1zpsP8LkStKA2JalB0NYzNKDDIx5YrpnJ30rPc8mbI4HFrRmen9E1/RLkqaFCZY0Op5IN2rSjXRtxp/XhsLVCEpyVJLrk5y/jOVJcnjr43JeksfOdozSMkw0cMT45jjnAA+pqt2Af6drhn7/ylXn0Q1IdABdk3lJmjYmWNKIqKp3VdXmVbVhVT2hqrxjO9o+S/cohmXZl+7h2TsDB9ONUikNgsV0w2yPmUc3utvvVdXtVXVne30ysFa6B673OoluMKfxD1WXpCkxwZKkEdQezHnzclbZHzimPYTzdGCTJBM9D0eabWcBOyfZsY10t4AuWfq9NuJd2uvd6X7vjH+Q7FHAe6rqp7MQs6QRMhSDXMydu3ntsP32K15Rkvrk7J+ce2NVrcxDrZdpu6xZ96z4MWnLdSO/uwC4p6foyKo6snedJDsA36iq3kcojC37BvD+qvpRm/8u8JaqWjSlwEbc3Llza4cdduh3GEPvtttu4+qrr6aqmDt3LltvvTU33HADAFtssQXXX389N9xwA0mYM2cO8+bNY4MNukci/uQnP+Exj3nMUvu74447uO6669hpp51m/VwkDa+zzz57wmv/mv0IZmXtsP32LPrRqf0OQ5KWKetv8ovp2tc9FH/B+itecTk+xR33VNX8KexiMv1ctJJ22GEHFi0yR5Wk1UGSCa/9Q5FgSdIoCQPRfnuF/VwkSdIDDcA1XJI0gE4CXtpGE9wDuK2qru13UJIkDTprsCRpAM3JRC30VsIKGvMlOQ7YE5ibZDFwGLAWQFUdQTd09X7AZcCvgZdPLSBJkkaDCZYkDZjZaCJYVQesYHkBr5nhMCRJWu2YYEnSAJozxQosh6OQJKk/7IMlSZIkSdPEGixJGkDe/ZIkaTiZYEnSgAmZ+iAXkiSpL/pykzTJPkkuSXJZkkP7EYMkDbI5U5wkSVJ/zPp1OMkawMeBfYFdgAOS7DLbcUiSJEnSdOtHE8Hdgcuq6nKAJMcD+wMX9iEWSRo4YRpGEZQkSX3Rj5Yk2wJX98wvbmVLSXJwkkVJFt1w402zFpwkDQKbCEqSNJz6cR2e6L7sA57YUlVHVtX8qpq/xdzNZyEsSZIkSZqafjQRXAxs1zM/D7imD3FI0mAKxFEEJUkaSv2owToL2DnJjknWBhYAJ/UhDkkaSMEmgpIkDatZr8GqqiVJXgucAqwBHFVVF8x2HJI0yBzkQsvy2Ytv7XcIWk297BGb9DsEabXQlwcNV9XJwMn9OLYkSZIkzZS+JFiSpOWzmZ8kScPJBEuSBkz3HCzbCEqSNIxMsCRpAFmDJUnScPIaLkmSJEnTxBosSRowXRPBfkchSZJWhQmWJA0gmxdIkjScTLAkaQDNwSosSZKGkTdJJUmSJGmaWIMlSQPGPliSJA0vEyxJGkA2L5AkaTiZYEnSgEmswZIkaVh5k1SSJEmSpok1WJI0gBxFUJKk4WSCJUkDyCaCkiQNJ5sISpIkSdI0McGSpAETui/nqUyjJMmVSX6a5Nwki1rZZkkWJrm0/d20Z/23JrksySVJ9u4pf1zbz2VJDk+SVr5Oki+28jOS7NCzzYHtGJcmOXAWT1uSNKBG7TosSUNhTqY2jaCnV9Wjq2p+mz8U+G5V7Qx8t82TZBdgAbArsA/wiSRrtG0+CRwM7NymfVr5QcAtVbUT8G/AB9q+NgMOA54A7A4c1pvISZJGkwmWJA2YEOZMcRL7A0e310cDz+spP76qflNVVwCXAbsn2RrYqKpOq6oCjhm3zdi+TgT2arVbewMLq+rmqroFWMj9SZkkaUSZYEmShl0B30lydpKDW9lWVXUtQPu7ZSvfFri6Z9vFrWzb9np8+VLbVNUS4DZg8+XsaylJDk6yKMmiG264YZVPUpI0HBxFUJIG0Ig281tVT66qa5JsCSxMcvFy1p3ona3llK/qNvcXVB0JHAkwf/78ByyXJK1erMGSpAGUKU6jpKquaX+vB75K1x/qutbsj/b3+rb6YmC7ns3nAde08nkTlC+1TZI1gY2Bm5ezL0nSCDPBkqQBExzkYrKSrJ9kw7HXwLOA84GTgLFR/Q4EvtZenwQsaCMD7kg3mMWZrRnhHUn2aP2rXjpum7F9PR/4XuundQrwrCSbtsEtntXKJEkjzCaCkqRhthXw1Tai+prAsVX17SRnASckOQi4CngBQFVdkOQE4EJgCfCaqrqv7etVwGeB9YBvtQngM8DnklxGV3O1oO3r5iTvBc5q672nqm6eyZOVJA0+EyxJGkCOBDg5VXU5sNsE5TcBey1jm/cB75ugfBHwyAnK76ElaBMsOwo4auWiliStzkywJGnAZMSa+UmStDoxwZKkAWQHWUmShpPXcEmSJEmaJtZgSdIAsoWgJEnDyQRLkgZMN0y7KZYkScPIJoKSJEmSNE2swZKkAWT9lSRJw8kES5IGkAmWJEnDyQRLkgaQCZYkScPJPliSJEmSNE2swZKkARRHEZQkaSiZYEnSgAk2EZQkaViZYEnSALL9tiRJw8lruCRJkiRNE2uwJGkA2QVLkqThZIIlSQMo9sKSJGkozXoTwSTbJfl+kouSXJDk9bMdgyQNskzDJEmS+qMfNVhLgH+oqnOSbAicnWRhVV3Yh1gkSZIkadrMeg1WVV1bVee013cAFwHbznYckjTIrMGSJGk49bUPVpIdgMcAZ/QzDkkaNHPMkiRJGkp9G6Y9yQbAl4G/q6rbJ1h+cJJFSRbdcONNsx+gJEmSJK2kviRYSdaiS66+UFVfmWidqjqyquZX1fwt5m4+uwFKUl9lyv9JkqT+mPUmgkkCfAa4qKo+PNvHl6RBZz8qSZKGVz9qsJ4MvAT4kyTntmm/PsQhSYMp3YOGpzJJkqT+mPUarKr6Ed6claS+S7IP8FFgDeDTVfX+ccs3Bj4PbE93vfhQVf3nrAcqSdIQ6dsgF5KkZZvpYdqTrAF8HNgX2AU4IMku41Z7DXBhVe0G7An8a5K1p3RikiSt5vo6TLskaWJzZr6if3fgsqq6HCDJ8cD+QO9D3wvYsPWd3QC4me5h8ZIkaRlMsCRpwEzTIBdzkyzqmT+yqo7smd8WuLpnfjHwhHH7+BhwEnANsCHwwqr63dRDkyRp9WWCJUmrpxurav5ylk+Uw9W4+b2Bc4E/AR4GLEzyPxM9u1CSJHXsgyVJA2gWRhFcDGzXMz+Prqaq18uBr1TnMuAK4BHTcX6SJK2uTLAkaQDN9CAXwFnAzkl2bANXLKBrDtjrKmAvgCRbAQ8HLl/1s5IkafVnE0FJGkCZ4UEuqmpJktcCp9AN035UVV2Q5JC2/AjgvcBnk/yULm97S1XdOKOBSZI05EywJOCQ9edxxF2L+x2GNKuq6mTg5HFlR/S8vgZ41mzHJUnSMDPBkqQBE2COj2OXJGkomWBJ0gAyv5IkaTiZYEnSADLBkiRpODmKoCRJkiRNE2uwJGkAzfQogpIkaWaYYEnSAJrkw4IlSdKAsYmgJEmSJE0Ta7AkacAE735JkjSsTLAkaQDZQlCSpOFkgiVJAyh2wpIkaSjZCkWSJEmSpok1WJI0gKy/kiRpOJlgSdKACSZYkiQNKxMsSRo0iX2wJEkaUvbBkiRJkqRpYg2WJA2gOVZgSZI0lEywJGkAxQxLkqShZIIlSQMmgF2wJEkaTvbBkiRJkqRpYg2WJA2aWIMlSdKwsgZLkgZQ2lDtqzqNkiRrJPlJkm+0+c2SLExyafu7ac+6b01yWZJLkuzdU/64JD9tyw5PexOTrJPki638jCQ79GxzYDvGpUkOnMVTliQNMBMsSdKwez1wUc/8ocB3q2pn4LttniS7AAuAXYF9gE8kWaNt80ngYGDnNu3Tyg8CbqmqnYB/Az7Q9rUZcBjwBGB34LDeRE6SNLpMsCRpACVTm0ZFknnAnwKf7ineHzi6vT4aeF5P+fFV9ZuqugK4DNg9ydbARlV1WlUVcMy4bcb2dSKwV6vd2htYWFU3V9UtwELuT8okSSPMPliSNIBGrZnfFHwEeDOwYU/ZVlV1LUBVXZtky1a+LXB6z3qLW9lv2+vx5WPbXN32tSTJbcDmveUTbCNJGmHWYEnSgBkbpt0arOVL8mzg+qo6e7KbTFBWyylf1W2WPmhycJJFSRbdcMMNkwpUkjS8TLAkScPqycBzk1wJHA/8SZLPA9e1Zn+0v9e39RcD2/VsPw+4ppXPm6B8qW2SrAlsDNy8nH09QFUdWVXzq2r+FltssWpnKkkaGiZYkjRoAnOSKU2joKreWlXzqmoHusErvldVfwWcBIyN6ncg8LX2+iRgQRsZcEe6wSzObM0J70iyR+tf9dJx24zt6/ntGAWcAjwryaZtcItntTJJ0oizD5YkDaARyZFmyvuBE5IcBFwFvACgqi5IcgJwIbAEeE1V3de2eRXwWWA94FttAvgM8Lkkl9HVXC1o+7o5yXuBs9p676mqm2f6xCRJg88ES5IGzug9y2qqqupU4NT2+iZgr2Ws9z7gfROULwIeOUH5PbQEbYJlRwFHrWrMkqTVk00EJUmSJGmaWIMlSQMmQLz9JUnSUDLBkqRBE5+DJUnSsDLBkqQBZH4lSdJw6lsjlCRrJPlJkm/0KwZJkiRJmk79rMF6PXARsFEfY5CkgWQTQUmShlNfarCSzAP+FPh0P44vSYMumdokSZL6o181WB8B3gxsuKwVkhwMHAyw/XbbzU5UkjQAAswxS5IkaSjNeg1WkmcD11fV2ctbr6qOrKr5VTV/i7mbz1J0kiRJkrTq+lGD9WTguUn2A9YFNkry+ar6qz7EIkmDx2Z+kiQNrVmvwaqqt1bVvKraAVgAfM/kSpKWlmRKkyRJ6o++DdMuSZIkSaubvj5ouKpOBU7tZwySNIishJIkaTj1NcGSJD1QMMGSJGlYmWBJ0qBJyBwzLEmShpF9sCRJkiRpmliDJUkDyCaCkiQNJxMsSRpAc8ywJEkaSiZYkjRgHORCkqThZR8sSZIkSZomJljLccj68/odwmpnEN/TQYxpuqwO57Y6nMOqSDKlSZIk9YdNBCVp0MQmgpIkDSsTLEkaQNZCSZI0nGwiKEmSJEnTxBosSRpAVmBJkjScTLAkacB0w7SbYUmSNIxsIihJkiRJ08QaLEkaNIF4+0uSpKFkgiVJA8dnWUmSNKxMsCRpEM0xwZIkaRjZCEWS1HdJXpBkw/b6HUm+kuSx/Y5LkqSVZYIlSYMomdo0fP6xqu5I8hRgb+Bo4JN9jkmSpJVmgiVJgybdMO1TmSZ1mGSfJJckuSzJoctYZ88k5ya5IMkPpvU8l3Zf+/unwCer6mvA2jN4PEmSZoR9sCRpEM1wH6wkawAfB54JLAbOSnJSVV3Ys84mwCeAfarqqiRbzmBIv0zyKeAZwAeSrIM3ASVJQ8iLlySNpt2By6rq8qq6Fzge2H/cOi8CvlJVVwFU1fUzGM9fAqfQJXO3ApsBb5rB40mSNCOswZKkgTMt/ajmJlnUM39kVR3ZM78tcHXP/GLgCeP28QfAWklOBTYEPlpVx0w1sF6tVuxtwE7AT4H/Bqiqa4Frp/NYkiTNBhMsSRowCWTqTQRvrKr5yzvMBGU1bn5N4HHAXsB6wGlJTq+qn001uB7HAGcD/w48GzgceNk07l+SpFllgiVJg2jmRwJcDGzXMz8PuGaCdW6sqruAu5L8ENgNmM4E68FV9fb2+pQk50zjviVJmnX2wZKk0XQWsHOSHZOsDSwAThq3zteApyZZM8mD6JoQXjTNcSTJpkk2S7IZsMa4eUmShoo1WJI0gKahieByVdWSJK+lG1hiDeCoqrogySFt+RFVdVGSbwPnAb8DPl1V509zKBvTNRHsPeGxWqwCHjrNx5MkaUaZYEnSIJqFhwVX1cnAyePKjhg3/y/Av8xgDDvM1L4lSeoHEyxJUl+1JoovBnalq7W6EDi2qn7T18AkSVoF9sGSpEGTdA8anso0JJLsQpdQ7QlcRTewxp7ABUl27V9kkiStGmuwJGkAZRaaCA6IfwdeVVULewuTPAP4GPD0vkQlSdIqsgZLkgbRiNRgAduOT64Aquq/gQf3IR5JkqbEBGsFDll/HoesP6/fYawWBvF9HMSYptvq8Bke9vi1XHOSrDO+MMm62MpCkjSETLAkadCErh/WVKbhcQzw5SQ7jBW01ycAn+tTTJIkrTLvDkrSAMqI3P6qqv/Xnsf1w/YwY4C7gA9V1b/3MTRJklaJCZYkDaLhqoWakqr6GPCxJBu2+TsAknyxql7Y1+AkSVpJJliSpIEwllj1eGJfApEkaQpMsCRp0CRkuEYClCRJjQmWJA2iEWkimOSxy1oErDWbsUiSNB1MsCRpEI1ODda/LmfZxbMWhSRJ08QES5LUN1X19H7HIEnSdOrLQMBJNklyYpKLk1yUxI7MktR0j7LKlKZhkeSfel4/cxW2XzfJmUn+L8kFSd7dyjdLsjDJpe3vpj3bvDXJZUkuSbJ3T/njkvy0LTs87Y1Msk6SL7byM8Y9s+vAdoxLkxy4im+DJGk10q8nrXwU+HZVPQLYDbioT3FI0mCak6lNw2OfntcfWIXtfwP8SVXtBjwa2CfJHsChwHeramfgu22eJLsAC4Bd27E/kWSNtq9PAgcDO7dpLLaDgFuqaifg38biTLIZcBjwBGB34LDeRE6SNJpmPcFKshHwNOAzAFV1b1XdOttxSNLgylg11qpPI6I6d7bZtdpUwP7A0a38aOB57fX+wPFV9ZuqugK4DNg9ydbARlV1WlUVcMy4bcb2dSKwV6vd2htYWFU3V9UtwEKWThglSSOoH32wHgrcAPxnkt2As4HXV9VdvSslOZjuTiLbb7fdrAcpSZoVWyb5e7pRA8de/15VfXhFO2g1UGcDOwEfr6ozkmxVVde2fVybZMu2+rbA6T2bL25lv22vx5ePbXN129eSJLcBm/eWT7BNb3z3X8+2335FpyNJGnKTrsFKsl6Sh0/DMdcEHgt8sqoeA9xFa7rRq6qOrKr5VTV/i7mbT8NhJWl4jEofLOA/gA2BDXpe904rVFX3VdWjgXl0tVGPXM7qE705tZzyVd2mN777r2dbbLGc0CRJq4NJ1WAleQ7wIWBtYMckjwbeU1XPXYVjLgYWV9UZbf5EJkiwJGlkhWHrR7XKqurd07ivW5OcStdM77okW7faq62B69tqi4HeZhHzgGta+bwJynu3WZxkTWBj4OZWvue4bU6drvORJA2nydZgvYuuA++tAFV1LrDDqhywqn4FXN1TG7YXcOGq7EuSNNqSbJFkk/Z6PeAZdM/POgkYG9XvQOBr7fVJwII2MuCOdINZnNmaE96RZI/Wv+ql47YZ29fzge+1flqnAM9Ksmkb3OJZrUySNMIm2wdrSVXdNo3NTl4HfCHJ2sDlwMuna8eStDoYsmZ+/bQ1cHTrhzUHOKGqvpHkNOCEJAcBVwEvAKiqC5KcQHdjbwnwmqq6r+3rVcBngfWAb7UJukGZPpfkMrqaqwVtXzcneS9wVlvvPVV184yerSRp4E02wTo/yYuANZLsDPwt8ONVPWirAZu/qttL0mpvRJoITlVVnQc8ZoLym+haSEy0zfuA901Qvgh4QP+tqrqHlqBNsOwo4KiVi1qStDqbbIL1OuDtdM8bOY6uCcR7ZyooSRppIzTU+vhRA8ebzCiCkiQNkkklWFX1a7oE6+0zG44kacSMjRT4cODxdP2dAJ4D/LAvEUmSNAWTHUXw6zxw6NnbgEXAp1rzCUnSNMmINBEcG0UwyXeAx1bVHW3+XcCX+hiaJEmrZLKjCF4O3En3jJL/AG4HrgP+oM1LkqbTWDPBVZ2Gz/bAvT3z97KKo9VKktRPk+2D9ZiqelrP/NeT/LCqnpbkgpkITJJG1gg9B6vH54Azk3yVrsXEnwHH9DckSZJW3mQTrC2SbF9VVwEk2R6Y25bdu+zNJElasap6X5JvAU9tRS+vqp/0MyZJklbFZBOsfwB+lOTndPdWdwRenWR94OiZCq5fDll/Xr9DWK0M4vs5iDFNp9Xx/HrP6Yi7Fvcxktkxos/BehBwe1X9Z3uA8I5VdUW/g5IkaWVMdhTBk9vzrx5Bl2Bd3DOwxUdmKDZJGlEZuSaCSQ6jez7iw4H/BNYCPg88uZ9xSZK0siZbgwWwM92Fb13gj5JQVbaPl6SZMHo1WH9G98DgcwCq6pokGy5/E0mSBs9kh2k/DNgT2AU4GdgX+BF2QJYkTY97q6qSFEBrgi5J0tCZ7DDtzwf2An5VVS8HdgPWmbGoJGmUhVEcpv2EJJ8CNknyN8B/A5/uc0ySJK20yTYRvLuqfpdkSZKNgOuBh85gXJI02oYzSVplVfWhJM+ke87iw4F3VtXCPoclSdJKm2yCtSjJJnQPFT6b7qHDZ85UUJKk0ZLkA1X1FmDhBGWSJA2NSTURrKpXV9WtVXUE8EzgwNZUUJI07QJz5kxtGj7PnKBs31mPQpKkKZrUVTjJd8deV9WVVXVeb5kkaZqNSB+sJK9K8lPg4UnO65muAM7rd3ySJK2s5TYRTLIu3YMf5ybZlK7rNcBGwDYzHJskjaaxQS5Gw7HAt4B/Bg7tKb+jqm7uT0iSJK26FfXBeiXwd3TJ1Nk95XcAH5+hmCRJI6KqbgNuAw4ASLIl3fMWN0iyQVVd1c/4JElaWStqIvhj4EnAG6vqocC7gfOBH9DddZQkzYQRaSI4JslzklwKXEF3jbmSrmZLkqShsqIE61PAb6rq35M8ja4Jx9F0dxuPnOngJGk0jeQgF/8P2AP4WVXtSPfsxf/tb0iSJK28FV2F1+hpA/9C4Miq+nJV/SOw08yGJkkjbMRqsIDfVtVNwJwkc6rq+8Cj+xyTJEkrbUV9sNZIsmZVLaG7m3jwSmwrSdJk3ZpkA+CHwBeSXA8s6XNMkiSttBUlSccBP0hyI3A38D8ASXaiayYoSZpuozWK4Jj9gXuANwAvBjYG3tPXiCRJWgXLTbCq6n3teVdbA9+pqmqL5gCvm+ngJGlkjViCVVV3ASTZCPh6n8ORJGmVrbCZX1WdPkHZz2YmHEnS7we5GCFJXklXY3U38Du6erwCHtrPuCRJWln2o5IkDYI3ArtW1Y39DkSSpKkwwZKkQTRiTQSBnwO/7ncQkiRNlQmWJA2a0Rzk4q3Aj5OcAfxmrLCq/rZ/IUmStPJMsCRJg+BTwPeAn9L1wZIkaSiZYEnSIBq9GqwlVfX3/Q5CkqSpMsGSpAETQkZsFEHg+0kOphuivbeJ4M39C0mSpJVngiVJg2j0arBe1P6+tafMYdolSUPHBGuSDll/3lLzR9y1uE+RDL/x7yUMxvu5uv8bD8P5TfTZ0Gioqh37HYMkSdPBBEuSBs0IjSKY5E+q6ntJ/nyi5VX1ldmOSZKkqTDBkqRBNCIJFvDHdKMHPmeCZQWYYEmShooJliQNnMCIDHJRVYe1l++pqit6lyWx2aAkaeiMxhVckjTovjxB2YmzHoUkSVNkDZYkDaIRaSKY5BHArsDG4/phbQSs25+oJEladSZYkjRoRmiQC+DhwLOBTVi6H9YdwN/0IyBJkqbCBEuSBtEsJFhJ9gE+CqwBfLqq3r+M9R4PnA68sKqmtdleVX0N+FqSJ1bVadO5b0mS+sE+WJI0gpKsAXwc2BfYBTggyS7LWO8DwCkzHNKfJdkoyVpJvpvkxiR/NcPHlCRp2plgSdLAaaMITmVasd2By6rq8qq6Fzge2H+C9V5HNwDF9dN3fhN6VlXdTtdccDHwB8CbZviYkiRNu74kWEnekOSCJOcnOS6JHZklqVcytQnmJlnUMx087gjbAlf3zC9uZT0hZFvgz4AjZvJUm7Xa3/2A46rq5lk4piRJ027W+2C1C/bfArtU1d1JTgAWAJ+d7VgkaSBNzyAXN1bV/BUcZbwaN/8R4C1VdV9mvk/Y15NcDNwNvDrJFsA9M31QSZKmW78GuVgTWC/Jb4EHAdf0KQ5JGlWLge165ufxwO/i+cDxLbmaC+yXZElV/dd0B1NVhyb5AHB7S+h+zcRNFiVJGmiz3kSwqn4JfAi4CrgWuK2qvjN+vSQHjzVtueHGm2Y7TEnqo1npg3UWsHOSHZOsTdeS4KTeFapqx6raoap2oHvo76unO7lK8uae2WdU1X3t2HfRtXaQJGmozHqClWRTuruSOwLbAOtPNFJUVR1ZVfOrav4Wczef7TAlqb+m3gdruapqCfBautEBLwJOqKoLkhyS5JAZPrteC3pev3Xcsn1mMQ5JkqZFP5oIPgO4oqpuAEjyFeBJwOf7EIskjayqOhk4eVzZhANaVNXLZiiMLOP1RPOSJA28fiRYVwF7JHkQXWfmvYBFfYhDkgbXLDxoeEDUMl5PNC9J0sCb9QSrqs5IciJwDrAE+Alw5GzHIUkDa3pGERwWuyW5ne6s12uvafM+wkOSNHT6MopgVR0GHNaPY0vS4MtkB6oYelW1Rr9jkCRpOo3GFVySJEmSZkG/noMlSVqe0WkiKEnSasUES5IGkQmWJElDySaCkjRoAmTO1KYRkWS7JN9PclGSC5K8vpVvlmRhkkvb3017tnlrksuSXJJk757yxyX5aVt2eNJluUnWSfLFVn5Gkh16tjmwHePSJAfO4qlLkgbU6FyFJUmroyXAP1TVHwJ7AK9JsgtwKPDdqtoZ+G6bpy1bAOxK9yDjTyQZG2jjk8DBwM5tGnvQ8UHALVW1E/BvwAfavjajG7DpCcDuwGG9iZwkaTSZYEnSwAnMmeI0Iqrq2qo6p72+A7gI2BbYHzi6rXY08Lz2en/g+Kr6TVVdAVwG7J5ka2Cjqjqtqgo4Ztw2Y/s6Edir1W7tDSysqpur6hZgIfcnZZKkETVyfbAOWX9ev0PQBCbz73LEXYtnIZL7TfazMttxTZfZfs/9f28ljVAzv+nSmu49BjgD2KqqroUuCUuyZVttW+D0ns0Wt7Lfttfjy8e2ubrta0mS24DNe8sn2KY3roPpasbYfvvtV/0EJUlDwSu4JA2iZGrTiEmyAfBl4O+q6vblrTpBWS2nfFW3ub+g6siqml9V87fYYovlhCZJWh2YYEmShlqSteiSqy9U1Vda8XWt2R/t7/WtfDGwXc/m84BrWvm8CcqX2ibJmsDGwM3L2ZckaYSZYEnSoElgzpypTSOi9YX6DHBRVX24Z9FJwNiofgcCX+spX9BGBtyRbjCLM1tzwjuS7NH2+dJx24zt6/nA91o/rVOAZyXZtA1u8axWJkkaYSPXB0uShsIINvNbRU8GXgL8NMm5rextwPuBE5IcBFwFvACgqi5IcgJwId0IhK+pqvvadq8CPgusB3yrTdAlcJ9LchldzdWCtq+bk7wXOKut956qunmGzlOSNCRMsCRJQ6uqfsTEfaEA9lrGNu8D3jdB+SLgkROU30NL0CZYdhRw1GTjlSSt/kywJGkQOYqgJElDyQRLkgaRTQQlSRpKJliSNGjGBrmQJElDxyu4JEmSJE0Ta7AkaRDZRFCSpKFkgiVJg8hBLiRJGkomWJI0aBKYYw2WJEnDyFukkiRJkjRNrMGSpEFkE0FJkoaSCZYkDSIHuZAkaSiZYEnSwIk1WJIkDSmv4JIkSZI0TazBkqRBExxFUJKkIWWCJUmDyD5YkiQNJZsISpIkSdI0sQZLkgaRg1xIkjSUTLAkadAk9sGSJGlImWBJ0iCyBkuSpKHkFVySJEmSpslQ1GD94ifnccj68/odhvpsUD8DgxrXdFidz23gOYqgJElDaSgSLEkaLbGJoCRJQ8oES5IGjQ8aliRpaHmLVJIkSZKmiTVYkjSIbCIoSdJQMsGSpEHkIBeSJA0lEyxJGjiBOdZgSZI0jLyCS5IkSdI0sQZLkgZNsImgJElDasZqsJIcleT6JOf3lG2WZGGSS9vfTWfq+JI01DJnapMkSeqLmbwKfxbYZ1zZocB3q2pn4LttXpK0lHQ1WFOZJElSX8xYglVVPwRuHle8P3B0e3008LyZOr4kSZIkzbbZ7oO1VVVdC1BV1ybZcpaPL0nDwVEEJUkaSgM7yEWSg4GDATbA5i6SRoiDXEiSNLRm+xbpdUm2Bmh/r1/WilV1ZFXNr6r565pgSZIkSRoCs51gnQQc2F4fCHxtlo8vSUMgjiIoSdKQmrEmgkmOA/YE5iZZDBwGvB84IclBwFXAC2bq+JI01GwiKEnSUJqxBKuqDljGor1m6piStNqwFkqSpKHkFVySJEmSpsnAjiIoSSMrgTk2EZQkaRiZYEnSILKJoCRJQ8kES5IGkYNcSJI0lLxFKkmSJEnTxBosSRo4sYmgJElDyiu4JA2gJFOaJEmrh29/+9s8/OEPZ6edduL973//A5ZffPHFPPGJT2SdddbhQx/60FLLkvCSl7zk9/NLlixhiy224NnPfvaMxz3KrMFaRYesP6/fIUgja7X//y9YgyVJ4r777uM1r3kNCxcuZN68eTz+8Y/nuc99Lrvsssvv19lss804/PDD+a//+q8HbL/++utz/vnnc/fdd7PeeuuxcOFCtt1221k8g9HkFVySJEkaQGeeeSY77bQTD33oQ1l77bVZsGABX/va15ZaZ8stt+Txj388a6211oT72HffffnmN78JwHHHHccBBxww43GPOhMsSRo4rQ/WVKbJHCXZJ8klSS5LcugEy1+c5Lw2/TjJbtN+qpKkZfrlL3/Jdttt9/v5efPm8ctf/nKl9rFgwQKOP/547rnnHs477zye8IQnTHeYGscmgpI0iGb4QcNJ1gA+DjwTWAycleSkqrqwZ7UrgD+uqluS7AscCXhllqRZUlUPKFvZfrZ/9Ed/xJVXXslxxx3HfvvtN12haTlMsCRpNO0OXFZVlwMkOR7YH/h9glVVP+5Z/3RgNe/8JkmDZd68eVx99dW/n1+8eDHbbLPNSu/nuc99Lm984xs59dRTuemmm6YzRE3ABEuSBtHUB7mYm2RRz/yRVXVkz/y2wNU984tZfu3UQcC3phqUJGnyHv/4x3PppZdyxRVXsO2223L88cdz7LHHrvR+XvGKV7DxxhvzqEc9ilNPPXX6A9VSTLAkadAEmPpQ6zdW1fwVHGW8B7ZFAZI8nS7BespUg5IkTd6aa67Jxz72Mfbee2/uu+8+XvGKV7DrrrtyxBFHAHDIIYfwq1/9ivnz53P77bczZ84cPvKRj3DhhRey0UYb/X4/8+bN4/Wvf32/TmPkmGBJ0sCZlQcNLwa265mfB1zzgEiSPwI+DexbVbYrkaRZtt9++z2g79Qhhxzy+9cPfvCDWbx48YTb3nnnnQ8o23PPPdlzzz2nNUYtzVEEJWk0nQXsnGTHJGsDC4CTeldIsj3wFeAlVfWzPsQoSdLQMcGSpEGUTG1agapaArwWOAW4CDihqi5IckiSsVuj7wQ2Bz6R5NxxfboGQpKjklyf5Pyess2SLExyafu7ac+yt7Zh6S9JsndP+eOS/LQtOzxtmK4k6yT5Yis/I8kOPdsc2I5xaZIDZ+mUJUkDziaCkjSIZr6JIFV1MnDyuLIjel7/NfDXMx7I1HwW+BhwTE/ZocB3q+r97flehwJvSbILXU3drsA2wH8n+YOqug/4JHAw3WiJJwP70A3qcRBwS1XtlGQB8AHghUk2Aw4D5tP1XTu7DXN/y4yfsTRC7jzyyBWvJK2CDQ4+eMb2bQ2WJA2apHsO1lSmEVFVPwRuHle8P3B0e3008Lye8uOr6jdVdQVwGbB7kq2BjarqtOoeOnPMuG3G9nUisFer3dobWFhVN7ekaiFdUiZJGnEmWJKk1c1WVXUtQPu7ZSufaGj6bdu0eILypbZpzSpvo2s2uax9PUCSg5MsSrLohhtumMJpSZKGgQmWJA2izJnapIksa2j65Q1ZvyrbLF1YdWRVza+q+VtsscWkApUkDS+vwpI0iGZ4kIvV3HWt2R/t7/WtfFlD0y9ur8eXL7VNkjWBjemaJE5qmHtJ0ugxwZKkgRNrsKbmJGBsVL8Dga/1lC9oIwPuCOwMnNmaEd6RZI/Wv+ql47YZ29fzge+1flqnAM9KsmkbpfBZrUySNOIcRVCSNLSSHAfsCcxNsphuZL/3AyckOQi4CngBQBuG/gTgQmAJ8Jo2giDAq+hGJFyPbvTAb7XyzwCfS3IZXc3Vgravm5O8l+55YgDvqarxg21IkkaQCZYkDSKb+U1KVR2wjEV7LWP99wHvm6B8EfDICcrvoSVoEyw7Cjhq0sFKkkaCCZYkDZpgMz9JkoaUCZYkDZzAHBMsSZKGkVdwSZIkSZom1mBJ0gCKfbAkSRpKJliSNIjsgyVJ0lDyCi5JkiRJ08QaLEkaNMFh2iVJGlImWJI0cGITQUmShpQJliQNImuwJEkaSt4ilSRJkqRpYg2WJA0iHzQsSdJQMsGSpEGT2ERQkqQhZYIlSYPIQS4kSRpKXsElSZIkaZpYgyVJg8gmgpIkDSUTLEkaSCZYkiQNoxlrIpjkqCTXJzm/p+xfklyc5LwkX02yyUwdX5KGV+4f6GJVJ0mS1Bcz2Qfrs8A+48oWAo+sqj8Cfga8dQaPL0mSJEmzasYSrKr6IXDzuLLvVNWSNns6MG+mji9JQ80aLEmShlI/+2C9AvjishYmORg4GGAD+yJIGjl+70mSNIz6Mkx7krcDS4AvLGudqjqyquZX1fx1/aEhSZIkaQjMeg1WkgOBZwN7VVXN9vElaeAFm/lJkjSkZjXBSrIP8Bbgj6vq17N5bEkaKuZXkiQNpZkcpv044DTg4UkWJzkI+BiwIbAwyblJjpip40vScMsUJ0mS1A8zVoNVVQdMUPyZmTqeJEmSJPVbP0cRlCRNyKHWJUkaViZYkjSITLAkSRpKJliSNJBMsCRJGkZ9eQ6WJEmSJK2OrMGSpEFkE0FJkoaSCZYkDSQTLEmShpEJliQNmjiKoCRJw8o+WJIkSZI0TazBkqRBZA2WJElDyQRLkgaSCZYkScPIJoKSJEmSNE2swZKkARSbCEqSNJRMsCRpEJlgSZI0lEywJGngBPtgSZI0nOyDJUmSJEnTxBosSRpENhGUJGkomWBJ0qAJJliSJA0pEyxJGkgmWJIkDSP7YEmSJEnSNLEGS5IGkU0EJUkaSiZYkjSIzK8kSRpKJliSNHB8DpYkScPKPliSJEmSNE2swZKkQWQfLEmShpIJliQNGp+DJUnS0DLBkqSBZIIlSdIwsg+WJEmSJE0Ta7AkaRDZRFCSpKFkgiVJAycmWJIkDSmbCErSiEqyT5JLklyW5NAJlifJ4W35eUke2484B9mK3kNJ0ugxwZKkgZQpTivYe7IG8HFgX2AX4IAku4xbbV9g5zYdDHxyiie1WpnkeyhJGjEmWJI0iJKpTSu2O3BZVV1eVfcCxwP7j1tnf+CY6pwObJJk6+k90aE2mfdQkjRihqIP1o387s5Pcecl/Y6jx1zgxn4HMc6gxWQ8KzZoMQ1aPDB4MS0vnodM10HO/sm5p2T9TeZOcTfrJlnUM39kVR3ZM78tcHXP/GLgCeP2MdE62wLXTjG21cVk3kOSHExXAwhwZ5JBup6t7gbtO2SgvbzfAWiq/LyvjFe+cjr2MuG1fygSLOCSqprf7yDGJFk0SPHA4MVkPCs2aDENWjwweDHNVjxVtc9MH4OJ2xHWKqwzyib1/rTE9sgJ1tUMG7TvEGkm+XkfHDYRlKTRtBjYrmd+HnDNKqwzynx/JEkPYIIlSaPpLGDnJDsmWRtYAJw0bp2TgJe20QT3AG6rKpsH3m8y76EkacQMSxPBQWtaMWjxwODFZDwrNmgxDVo8MHgxDVo8q6yqliR5LXAKsAZwVFVdkOSQtvwI4GRgP+Ay4NfYRWMpy3oP+xyWlrba/D8rTYKf9wGRKpvTS5IkSdJ0sImgJEmSJE0TEyxJkiRJmiYDnWAl2SfJJUkuS3LoDB/rqCTXJzm/p2yzJAuTXNr+btqz7K0trkuS7N1T/rgkP23LDk8m98TPCeLZLsn3k1yU5IIkr+9nTEnWTXJmkv9r8by73+9R29caSX6S5BsDEs+VbV/njj2DqM+fo02SnJjk4vZZemKf43l4e2/GptuT/F2fY3pD+0yfn+S49lnv6+dIGiVJKsm/9sy/Mcm7VrDNczMNvwuSvCzJDT3fSce08s8muaKn/LCe179K8sue+bWnGodGV5Ktkhyb5PIkZyc5LcmfJdmz/b9xUM+6j2llb0zy8fb5uzDJ3T2fx+eP23/v75JzkzwpyQ7jthn/Gb+v5/Xfzv67shqoqoGc6DoM/xx4KLA28H/ALjN4vKcBjwXO7yn7IHBoe30o8IH2epcWzzrAji3ONdqyM4En0j0f5VvAvqsYz9bAY9vrDYGfteP2Jaa27Qbt9VrAGcAe/XyP2r7+HjgW+Ea//83avq4E5o4r6+fn6Gjgr9vrtYFN+v0e9cS2BvAruof09etzvS1wBbBemz8BeNmgvEdOTqMwAfe0/w/ntvk3Au+apWO/DPjYBOWfBZ6/jG3eBbyx3++b0/BP7XpxGnBIT9lDgNcBewLnAd/pWfYB4Nzezx+wAz2/XSc4xpU88HfJira5s9/vzbBPg1yDtTtwWVVdXlX3AscD+8/Uwarqh8DN44r3p/uBSvv7vJ7y46vqN1V1Bd0IW7sn2RrYqKpOq+4TekzPNisbz7VVdU57fQdwEd2Pwb7EVJ072+xabap+xQOQZB7wp8Cne4r7Fs9y9CWmJBvR3Tj4DEBV3VtVt/YrngnsBfy8qn7R55jWBNZLsibwILrnGA3KeySNgiV0o5+9YfyCJM9Jcka6lgr/nWSrVv6yJB9LsnG7Qz+nlT8oydVJ1krysCTfbrUC/5PkEbN7WtIK/Qlwb3WjtgJQVb+oqn9vs1cB67ZargD70N3A04Ab5ARrW+DqnvnFrWw2bVXtmS/t75YriG3b9np8+ZQk2QF4DF2tUd9iStcc71zgemBhVfU1HuAjwJuB3/WU9fvfrIDvtAv6wX2O6aHADcB/th8nn06yfh/jGW8BcFx73ZeYquqXwIfoLmLX0j3n6Tv9ikcaYR8HXpxk43HlPwL2qKrH0N1ofXPvwqq6ja5W+Y9b0XOAU6rqt3RJ2+uq6nF0tWKfWMaxX9jTHKr3UQT/0lP+qCmdnTSxXYFzVrDOicALgCe1dX+zCsf5fvscn9FT9rCez/fHV2GfWo5Bfg7WRP0XBmVM+WXFNu0xJ9kA+DLwd1V1+3K6dcx4TFV1H/DoJJsAX03yyOWsPqPxJHk2cH1VnZ1kz8lsMpPx9HhyVV2TZEtgYZKL+xjTmnTNXl9XVWck+Shdc7d+xXP/gbo+C88F3rqiVWcypnR9q/ana+53K/ClJH/Vr3ikUdWub8cAfwvc3bNoHvDFVku8Nl1TwvG+CLwQ+D7djZtPtGvnk+j+nx5bb51lHP6LVfXaCcrfVFUnrvTJSKuoJTpPAe4F3tSKT6D7jD+C7qbkk1Zh10+vqhvHlf28qh69iqFqBQa5BmsxsF3P/Dy6pjuz6br2pU77e/0KYlvcXo8vXyVJ1qJLrr5QVV8ZhJgAWjOzU+mqqvsVz5OB5ya5ku6u5p8k+Xwf4wGgqq5pf68HvkrX1LVfMS0GFreaRujugj22j/H02hc4p6qua/P9iukZwBVVdUO74/0VuovXILxH0qj5CHAQsH5P2b/T9ZF6FPBKYN0JtjsJ2DfJZsDjgO/R/b65taoe3TP94YxGL628C+iuywBU1Wvoms9v0VP2K+C3wDOB7y5vZ2Mtjdr0npkJWZMxyAnWWcDOSXZsd7sX0H2JzqaTgAPb6wOBr/WUL0iyTpIdgZ2BM1tTojuS7NHayr60Z5uV0rb/DHBRVX243zEl2aLVXJFkPbofphf3K56qemtVzauqHeg+G9+rqr/qVzwASdZPsuHYa+BZwPn9iql9KV+d5OGtaC/gwn7FM84B3N88cOzY/YjpKmCP1m8jdO/RRX2MRxpZVXUz3d36g3qKNwZ+2V4f+ICNuu3upBtk5qN0Ax7dV1W3A1ckeQF019Qku81Y8NKq+R5dH6tX9ZQ9aIL13gm8pbUkWqb22R+7ofDO6QxUK2dgmwhW1ZIkrwVOoRtt7KiqumCmjpfkOLoRW+YmWQwcBrwfOCHdEJlX0bWBpaouSHIC3Y/VJcBrej70r6IbfWg9uo6Iq9oZ8cnAS4Cftn5PAG/rY0xbA0cnWYMuMT+hqr6R5LQ+xbMs/fw324qu6SR0/28dW1XfTnJWH2N6HfCFdpPicuDltH+/fv2bJXkQ3Z24V/YU9+XfrTWdPJGuXfsS4Cd0/TY26Ec8kvhXoLe53rvomvn9EjidrjnvRL4IfInuOj7mxcAnk7yDbmCm4+n6a0kDoaoqyfOAf0vyZrp+03cBbxm33o/7EJ6mIN2AV5IkSZKkqRrkJoKSJEmSNFRMsCRJkiRpmphgSZIkSdI0McGSJEmSpGligiVJkiRJ08QES0MvyZ0ruf6eSb4xU/FIkiRpdJlgSZIkSdI0McHSaqPVTJ2a5MQkFyf5QtpTf5Ps08p+BPx5zzbrJzkqyVlJfpJk/1Z+eJJ3ttd7J/lhEv9/kSRJ0nKt2e8ApGn2GGBX4Brgf4EnJ1kE/AfwJ8BlwBd71n878L2qekWSTYAzk/w3cChwVpL/AQ4H9quq383eaUiSJGkYeUdeq5szq2pxS4bOBXYAHgFcUVWXVlUBn+9Z/1nAoUnOBU4F1gW2r6pfA38DLAQ+VlU/n7UzkCRJ0tCyBkurm9/0vL6P+z/jtYz1A/xFVV0ywbJHATcB20xfeJIkSVqdWYOlUXAxsGOSh7X5A3qWnQK8rqev1mPa34cA/0DX5HDfJE+YxXglSZI0pEywtNqrqnuAg4FvtkEuftGz+L3AWsB5Sc4H3tuSrc8Ab6yqa4CDgE8nWXeWQ5ckSdKQSdclRZIkSZI0VdZgSZIkSdI0McGSJEmSpGligiVJkiRJ08QES5IkSZKmiQmWJEmSJE0TEyxJkiRJmiYmWJIkSZI0Tf4/8NmjWZDXes4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from typing import List, Tuple\n",
    "import time\n",
    "\n",
    "# ----------------------------\n",
    "# 1. 生成极度稀疏信号（雷达脉冲）\n",
    "# ----------------------------\n",
    "def generate_sparse_signal(N=8192, num_pulses=3):\n",
    "    \"\"\"生成 N 点信号，仅 num_pulses 个非零点\"\"\"\n",
    "    x = np.zeros(N, dtype=complex)\n",
    "    indices = np.random.choice(N, num_pulses, replace=False)\n",
    "    x[indices] = np.random.randn(num_pulses) + 1j * np.random.randn(num_pulses)\n",
    "    return x\n",
    "\n",
    "# ----------------------------\n",
    "# 2. 标准迭代 FFT（Python 实现，用于公平对比）\n",
    "# ----------------------------\n",
    "def naive_fft(x: np.ndarray) -> np.ndarray:\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N & (N - 1) != 0:\n",
    "        return np.fft.fft(x)  # 当N不是2的幂时，使用numpy的FFT作为备选\n",
    "    \n",
    "    # 位反转（修正了原代码中的错误）\n",
    "    num_bits = N.bit_length() - 1\n",
    "    # 生成位反转索引列表\n",
    "    rev_indices = [sum(((n >> i) & 1) << (num_bits - 1 - i) for i in range(num_bits)) for n in range(N)]\n",
    "    x = x[rev_indices]  # 应用位反转\n",
    "    \n",
    "    # 迭代FFT计算\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s  # 2^s\n",
    "        w_m = np.exp(-2j * np.pi / m)  # 旋转因子\n",
    "        for k in range(0, N, m):\n",
    "            w = 1.0  # 初始化旋转因子\n",
    "            for j in range(m // 2):\n",
    "                # 蝴蝶操作\n",
    "                t = w * x[k + j + m // 2]\n",
    "                u = x[k + j]\n",
    "                x[k + j] = u + t\n",
    "                x[k + j + m // 2] = u - t\n",
    "                w *= w_m  # 更新旋转因子\n",
    "    return x\n",
    "\n",
    "# ----------------------------\n",
    "# 3. GMT-FFT with pruning (理论验证版)\n",
    "# ----------------------------\n",
    "def gmt_fft_pruned(x: np.ndarray, eps=1e-8) -> Tuple[np.ndarray, List[set], int]:\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    if N & (N - 1) != 0:\n",
    "        X = np.fft.fft(x)\n",
    "        return X, [set(range(N))], N * N  # 当N不是2的幂时，使用numpy的FFT作为备选\n",
    "    \n",
    "    num_bits = N.bit_length() - 1\n",
    "    # 位反转\n",
    "    rev_indices = [sum(((n >> i) & 1) << (num_bits - 1 - i) for i in range(num_bits)) for n in range(N)]\n",
    "    x = x[rev_indices]\n",
    "    \n",
    "    active_sets = []\n",
    "    # 初始活跃节点：模大于eps的点\n",
    "    active = set(np.nonzero(np.abs(x) > eps)[0])\n",
    "    active_sets.append(active.copy())\n",
    "    \n",
    "    flops_count = 0  # 手动计数FLOPs\n",
    "    \n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        next_active = set()\n",
    "        \n",
    "        for k in range(0, N, m):\n",
    "            # 检查当前块是否有活跃节点\n",
    "            block_active = any(idx in active for idx in range(k, k + m))\n",
    "            if not block_active:\n",
    "                continue\n",
    "            \n",
    "            w = 1.0\n",
    "            for j in range(m // 2):\n",
    "                idx1 = k + j\n",
    "                idx2 = k + j + m // 2\n",
    "                # 仅处理有活跃节点的位置\n",
    "                if idx1 in active or idx2 in active:\n",
    "                    t = w * x[idx2]\n",
    "                    u = x[idx1]\n",
    "                    x[idx1] = u + t\n",
    "                    x[idx2] = u - t\n",
    "                    next_active.add(idx1)\n",
    "                    next_active.add(idx2)\n",
    "                    flops_count += 6  # 估算：复数乘+加+减 ≈ 6 FLOPs\n",
    "                w *= w_m\n",
    "        \n",
    "        active = next_active\n",
    "        active_sets.append(active.copy())\n",
    "    \n",
    "    return x, active_sets, flops_count\n",
    "\n",
    "# ----------------------------\n",
    "# 4. 主实验：FLOPs 对比 + 可视化\n",
    "# ----------------------------\n",
    "def main():\n",
    "    N = 8192\n",
    "    x = generate_sparse_signal(N, num_pulses=5)  # 仅5个非零点\n",
    "    non_zero_ratio = np.count_nonzero(x) / N * 100\n",
    "    \n",
    "    print(f\"Signal Length: {N}\")\n",
    "    print(f\"Non-zero ratio: {non_zero_ratio:.4f}%\")\n",
    "    \n",
    "    # 标准FFT (Python实现)\n",
    "    start = time.time()\n",
    "    X1 = naive_fft(x)\n",
    "    t_naive = time.time() - start\n",
    "    \n",
    "    # GMT-FFT (带剪枝)\n",
    "    start = time.time()\n",
    "    X2, trace, flops_gmt = gmt_fft_pruned(x, eps=1e-5)\n",
    "    t_gmt = time.time() - start\n",
    "    \n",
    "    # 手动估算标准FFT的FLOPs\n",
    "    flops_naive = 5 * N * (N.bit_length() - 1)  # 约等于5*N*log2(N)\n",
    "    \n",
    "    speedup_flops = flops_naive / flops_gmt\n",
    "    error = np.max(np.abs(X1 - X2))\n",
    "    \n",
    "    print(f\"Naive FFT  FLOPs: {flops_naive:,}\")\n",
    "    print(f\"GMT-FFT    FLOPs: {flops_gmt:,}\")\n",
    "    print(f\"FLOPs Speedup: {speedup_flops:.2f}x\")\n",
    "    print(f\"Max error: {error:.2e}\")\n",
    "    \n",
    "    # ----------------------------\n",
    "    # 可视化\n",
    "    # ----------------------------\n",
    "    plt.figure(figsize=(12, 6))\n",
    "    \n",
    "    # 活跃节点热力图\n",
    "    plt.subplot(1, 2, 1)\n",
    "    num_stages = len(trace)\n",
    "    heatmap = np.zeros((num_stages, N))\n",
    "    for stage, active in enumerate(trace):\n",
    "        for idx in active:\n",
    "            heatmap[stage, idx] = 1\n",
    "    plt.imshow(heatmap, aspect='auto', cmap='Reds', interpolation='none')\n",
    "    plt.xlabel('Index')\n",
    "    plt.ylabel('Stage')\n",
    "    plt.title(f'GMT-FFT Active Nodes\\n({len(trace[-1])} active in last stage)')\n",
    "    plt.colorbar()\n",
    "    \n",
    "    # FLOPs对比柱状图\n",
    "    plt.subplot(1, 2, 2)\n",
    "    labels = ['Naive FFT', 'GMT-FFT']\n",
    "    flops = [flops_naive, flops_gmt]\n",
    "    plt.bar(labels, flops, color=['skyblue', 'lightcoral'], alpha=0.8)\n",
    "    plt.ylabel('Estimated FLOPs')\n",
    "    plt.title(f'Computational Saving\\n{speedup_flops:.2f}× FLOPs reduction')\n",
    "    for i, v in enumerate(flops):\n",
    "        plt.text(i, v * 1.05, f'{v/1e6:.1f}M', ha='center')\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.savefig('gmt_fft_theoretical_gain.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然后让GMT-FFT的执行过程完整可视化，这是GMT理论最大的大杀器，超级大杀器"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original non-zero indices: [362, 3762, 5355, 5592, 7744]\n",
      "Initial non-zero indices (bit-reversed): [79, 885, 2478, 2768, 6885]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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A8ES4/gng5HB5APCMuxe5+0/ALOAAM+sCZLr7x+7uwJMx+4iIiIg0OiXr1jFx0CDKSkrY78or6dG3b9SRUkrCRpDd/Wczux2YB6wFJrv7ZDPr7O6Lwm0WmVmncJduBCPE5RaEbevD5crtmzCzYQQjzWRlZZGXl1eXH2mz8vPzk/p+jZ36O3nU18mjvk4e9XXyqK/r3pQ//5lfcnNp26sXvYcPr6h51Nd1I5FTLNoRjApvD6wEnjOz82rapYo2r6F900b3UcAogJycHI/iTwwN6c8aqUD9nTzq6+RRXyeP+jp51Nd1Z9677zL9wQex9HROGDeO7bp332i9+nrrJXKKxdHAT+6+zN3XAy8ChwBLwmkThM9Lw+0XALE/4SyCKRkLwuXK7SIiIiKNStGqVbx+/vngzkE33USX/fePOlJKSmSBPA84yMxahled6AvMACYAQ8JthgAvh8sTgLPNrJmZbQ/0Aj4Lp2MUmNlB4XEGx+wjIiIi0mi8c801rJo7l859+nDQiBFRx0lZiZyD/KmZPQ9MA0qALwimP7QGxpvZRQRF9Bnh9tPDK13khttfFl7BAuB3wGigBcHVK3QFCxEREWlUZk2YwLePPUZ6s2YcP2YM6U2aRB0pZSX0Tnru/hfgL5WaiwhGk6vafiSwydWh3X0qsEedBxQRERFpANYsW8bkoUMBOOKWW9h2t90iTpTadCc9ERERkXrM3Xnz4otZs3Qp3Y88kv2uvDLqSClPBbKIiIhIPZY7diwz//MfmrZpQ//Ro7E0lW+Jph4WERERqadWzZvHW5dfDsBR99xD2x49Ik7UOKhAFhEREamHvKyM1y+4gOJVq9hpwAB2HzJk8ztJnVCBLCIiIlIPffHvfzPv7bdp0bEjx4waRXC1W0kGFcgiIiIi9cwv333H+3/4AwD9Hn6YVp06RZyocVGBLCIiIlKPlK5fz8RBgyhZt47dzz+fnQYMiDpSo6MCWURERKQe+fQf/2DJ1Km0yc7mqLvuijpOo6QCWURERKSeWDx1Kp/cfDMAx40eTbO2bSNO1DipQBYRERGpB9avXcvEwYMpKymhz9VXk/3rX0cdqdFSgSwiIiJSD3wwYgTLZ8yg/a67ctjf/x51nEZNBbKIiIhIxOa98w6f/+tfWHo6x48ZQ5MWLaKO1KipQBYRERGJUFF+PpPOPx+Ag//0J7bLyYk2kKhAFhEREYnS21dfTcG8eXTOyeHAP/4x6jiCCmQRERGRyMx86SWmjx5NRvPmHD9mDOlNmkQdSVCBLCIiIhKJwqVLmTxsGABH/POfbLvrrhEnknIqkEVERESSzN15c9gw1i5bRvZRR7Hv5ZdHHUliqEAWERERSbLpTz7JrJdfpmlmJv0ffxxLU0lWn+inISIiIpJE+XPn8vaVVwLQ9957yczOjjiRVKYCWURERCRJvKyM1y+4gOJVq+h1yin0HjQo6khSBRXIIiIiIkky7Z57mP/OO7Ts1IljHnoIM4s6klRBBbKIiIhIEuTl5vL+DTcAcOyoUbTs2DHiRFIdFcgiIiIiCVa6fj2TBg+mtKiIPS64gJ0GDIg6ktRABbKIiIhIgn0yciRLPv+czB49+PVdd0UdRzZDBbKIiIhIAi2aMoVP/vY3MKP/6NE0y8yMOpJshgpkERERkQRZv3YtkwYNwktL6XPNNWQfeWTUkSQOKpBFREREEuR/N97I8u+/Z9vevTl85Mio40icVCCLiIiIJMC8t99m2t13k5aRwXFPPklG8+ZRR5I4qUAWERERqWPrVq5k0vnnA3Dwn//Mdn36RBtIakUFsoiIiEgde/uqqyiYP5/tDjiAA2+8Meo4UksqkEVERETq0A8vvkhuOKXi+CefJC0jI+pIUksqkEVERETqSOGSJbx58cUAHHHrrbTfZZeIE8mWUIEsIiIiUgfcnclDh7I2L4/svn3Z97LLoo4kW0gFsoiIiEgd+Hb0aH585RWatW1L/8cfx9JUZjVU+smJiIiIbKX8OXN456qrADjq3nvJ7N494kSyNVQgi4iIiGwFLytj0vnnU1xQQK9TT6X3eedFHUm2kgpkERERka3w+d13s+C992jZuTPHPPggZhZ1JNlKKpBFREREtlDe9On8L7zOcb+HH6Zlx44RJ5K6oAJZREREZAuUFhczcdAgSouK2POii9jxxBOjjiR1RAWyiIiIyBb4+G9/Y+kXX5DZsydH3nln1HGkDqlAFhEREamlRZ9+yqd//zuYcdzo0TTLzIw6ktQhFcgiIiIitbB+zRomDh6Ml5aSc+21dP/Vr6KOJHVMBbKIiIhILbx/ww2s+OEHtu3dm8P+9reo40gCqEAWERERidPc//6XL+69l7SMDI4fM4aM5s2jjiQJoAJZREREJA7rVq7k9QsuAODgv/yFzvvtF3EiSRQVyCIiIiJxePvKKylYsIAuBx7IgTfcEHUcSSAVyCIiIiKb8cMLL5A7ZgwZLVpw3JNPkpaREXUkSSAVyCIiIiI1KFy8mDcvvhiAX912G+133jniRJJoKpBFREREquHuvDF0KGt/+YUexxzDPr/7XdSRJAlUIIuIiIhU49vHHmP2q6/SrG1b+j/2GJam0qkx0E9ZREREpAorf/qJt6++GoC+991Hm6ysaANJ0qhAFhEREYmRO24cD/XowSM77MD61avZ7oAD2O3cc6OOJUmkAllEREQklDtuHJOHDaNg3ryKtrxvvmHGU09FmEqSTQWyiIiISOiDESMoWbNmo7aStWv5YMSIiBJJFFQgi4iIiIRWxYwcx9MuqSmhBbKZbWNmz5vZd2Y2w8wONrP2Zvammc0Mn9vFbH+jmc0ys+/NrF9Mex8z+yZcd4+ZWSJzi4iISOPUulu3Ktszs7OTnESilOgR5LuB1919V2BvYAZwA/CWu/cC3gpfY2a9gbOB3YH+wP1mlh4e5wFgGNArfPRPcG4RERFphLoccMAmbRktW3LYyJERpJGoJKxANrNM4AjgUQB3L3b3lcAA4IlwsyeAk8PlAcAz7l7k7j8Bs4ADzKwLkOnuH7u7A0/G7CMiIiJSJ9avWcOC994DoGXnzmBGZo8eHDtqFL0HDow4nSRTIm8kvgOwDHjczPYGPgeuAjq7+yIAd19kZp3C7bsBn8TsvyBsWx8uV24XERERqTPfjh7N2l9+oXNODud99hma0dl4JbJAzgD2A65w90/N7G7C6RTVqOpb6DW0b3oAs2EEUzHIysoiLy+vdom3Un5+flLfr7FTfyeP+jp51NfJo75OnobQ12WlpXx2220A7HbJJfzyyy8RJ9oyDaGvG4JEFsgLgAXu/mn4+nmCAnmJmXUJR4+7AEtjtu8es38WsDBsz6qifRPuPgoYBZCTk+MdOnSoq88StyjeszFTfyeP+jp51NfJo75Onvre198/9xwFc+bQdocd2O/880lLT9/8TvVUfe/rhiBhc5DdfTEw38x2CZv6ArnABGBI2DYEeDlcngCcbWbNzGx7gpPxPgunYxSY2UHh1SsGx+wjIiIislXcnSnh6HHOddc16OJY6sZmR5DN7AyCK1EUmNlNBNMm/ubu0+I4/hXAODNrCswGLiAoyseb2UXAPOAMAHefbmbjCYroEuAydy8Nj/M7YDTQApgUPkRERES22vz33mPxlCm06NCBPc4/P+o4Ug/EM8XiT+7+nJkdBvQDbie47NqBm9vR3b8EcqpY1bea7UcCm1xHxd2nAnvEkVVERESkVspHj/e9/HKatGwZcRqpD+KZYlE+ivsb4AF3fxlomrhIIiIiIsmx7Ntv+WniRDJatGCfyy6LOo7UE/EUyD+b2UPAmcBEM2sW534iIiIi9drU228HYI8LLqClTm6TUDyF7pnAG0D/8EYf7YHfJzKUiIiISKIVLFjAjKeewtLSyLn22qjjSD2y2QLZ3dcQXIrtsLCpBJiZyFAiIiIiifb53XdTtn49vU47jW123DHqOFKPbLZANrO/AH8AbgybmgBjExlKREREJJGK8vP5+qGHANj/9/rDuGwsnikWpwAnAYUA7r4QaJPIUCIiIiKJ9NVDD1FcUED3I4+ky/77Rx1H6pl4CuRid3fC2zubWavERhIRERFJnNLiYqbdfTeg0WOpWjwF8vjwKhbbmNlQ4L/Aw4mNJSIiIpIYM556itULF9Jhjz3Y/rjjoo4j9dBmbxTi7reb2THAKmAX4M/u/mbCk4mIiIjUMS8r23Bb6eHDMbOIE0l9FM+d9AgLYhXFIiIi0qDNnjSJX3Jzad2tG7udc07UcaSeqrZANrMCwnnHVXH3zIQkEhEREUmQKbfeCkCfq68mvaluDCxVq7ZAdvc2AGb2/4DFwBjAgIHoKhYiIiLSwCz67DMWvP8+TTMz2WvYsKjjSD0Wz0l6/dz9fncvcPdV7v4AcFqig4mIiIjUpfK5x3tfcgnNMvWHcKlePAVyqZkNNLN0M0szs4FAaaKDiYiIiNSVFbNm8cMLL5DWpAl9rroq6jhSz8VTIJ8LnAksIbjl9Blhm4iIiEiDMPXOO8Gd3uedR+uuXaOOI/VcPJd5mwMMSHwUERERkbpXuHQp0x9/HAgu7SayOZsdQTazLDP7j5ktNbMlZvaCmWUlI5yIiIjI1vryvvsoWbeOHU44gQ69e0cdRxqAeKZYPA5MALoC3YBXwjYRERGReq24sJAv77sP0G2lJX7xFMgd3f1xdy8JH6OBjgnOJSIiIrLVvn38cdb+8gvbHXAAWYcfHnUcaSDiKZDzzOy88CoW6WZ2HvBLooOJiIiIbI2ykhI+v/NOAA64/nrdVlriFk+BfCHBVSwWA4uA08M2ERERkXrrhxdeIP+nn9hmp53Y6eSTo44jDUg8V7GYB5yUhCwiIiIidcLdK24MknPddaSlp0ecSBqSagtkM/tzDfu5u9+cgDwiIiIiW23+u++y5PPPadGxI7sPGRJ1HGlgahpBLqyirRVwEbAtoAJZRERE6qXPbr0VgP2uuIImLVpEnEYammoLZHe/o3zZzNoAVwEXAM8Ad1S3n4iIiEiUln39NXNef52Mli3Z59JLo44jDVCNc5DNrD1wLTAQeALYz91XJCOYiIiIyJaYcvvtAOx54YW02HbbiNNIQ1TTHOTbgFOBUcCe7r46aalEREREtsCq+fP57umnsbQ0+lx7bdRxpIGq6TJv1xHcPe8mYKGZrQofBWa2KjnxREREROI37e67KSspYeczzmCb7bePOo40UDXNQY7nGskiIiIi9cK6lSv56qGHAN1WWraOimARERFJCV899BDrV68m+6ij2K5Pn6jjSAOmAllEREQavJKiIqbddReg0WPZeiqQRUREpMGbMW4chYsX02HPPenZr1/UcaSBi6tANrMeZnZ0uNwivC6yiIiISOS8rKzi0m77//73mFnEiaSh22yBbGZDgeeBh8KmLOClBGYSERERidvs115j+YwZtOnenV3PPjvqOJIC4hlBvgw4FFgF4O4zgU6JDCUiIiISrym33QZAn6uvJr1Jk4jTSCqIp0Aucvfi8hdmlgF44iKJiIiIxGfhJ5+w4H//o1nbtuw1dGjUcSRFxFMgv2dmfwRamNkxwHPAK4mNJSIiIrJ55aPHe//udzRto1OkpG7EUyDfACwDvgEuBiYS3F1PREREJDIrZs5k5n/+Q3rTpux35ZVRx5EUUu2d9GIMAJ5094cTHUZEREQkXlPvuAPc6T1oEK27dIk6jqSQeEaQTwJ+MLMxZvabcA6yiIiISGQKly7l29GjAci57rpow0jK2WyB7O4XADsRzD0+F/jRzB5JdDARERGR6nzx739TWlTEjiedxLa77RZ1HEkxcY0Gu/t6M5tEcPWKFgTTLn6byGAiIiIiVSkuLOTL++4DdFtpSYx4bhTS38xGA7OA04FHAE30ERERkUh8+9hjrFu+nC4HHUS3Qw+NOo6koHhGkM8HngEudveixMYRERERqV5ZSQlT77wTgAOuv163lZaE2GyB7O66Z6OIiIjUCz88/zyr5syhXa9e7HjSSVHHkRRVbYFsZh+4+2FmVsDGd84zwN09M+HpRERERELuXnFjkJzhw0lLT484kaSqagtkdz8sfNZtaURERCRy895+myXTptGyUyd2Hzw46jiSwuI5SW9MPG0iIiIiiVQ+erzflVeS0bx5xGkklcVzo5DdY1+ENwrpk5g4IiIiIpta+tVXzHnjDZq0asXev/td1HEkxVVbIJvZjeH8473MbFX4KACWAC8nLaGIiIg0elNvvx2APS+6iBbt20ecRlJdtQWyu/8jnH98m7tnho827r6tu9+YxIwiIiLSiK2aN4/vnnkGS0+nzzXXRB1HGoF4plh8ZmZty1+Y2TZmdnLiIomIiIhs8Pldd1FWUsIuZ55J2549o44jjUA8BfJf3D2//IW7rwT+krBEIiIiIqF1K1bw9cMPA7qttCRPPAVyVdvEcwc+ERERka3y1YMPsn71anocfTSd99036jjSSMRTIE81szvNbEcz28HM/gV8nuhgIiIi0riVFBUx7Z57ANj/+usjTiONSTwF8hVAMfAs8BywFrg0kaFEREREZowdS+HixXTaZx96HH101HGkEdlsgezuhe5+g7vnuHsf4EHgsnjfwMzSzewLM3s1fN3ezN40s5nhc7uYbW80s1lm9r2Z9Ytp72Nm34Tr7jEzq93HFBERkYbEy8o2uq20/umXZIpnBBkz62BmvzOz94F3gM61eI+rgBkxr28A3nL3XsBb4WvMrDdwNsGNSfoD95tZ+U3WHwCGAb3CR/9avL+IiIg0MD+++irLv/+eNtnZ7HLmmVHHkUamphuFtDGzwWb2OvAZsBOwg7vv6O7D4zm4mWUBvwEeiWkeADwRLj8BnBzT/oy7F7n7T8As4AAz6wJkuvvH7u7AkzH7iIiISAqacuutAORccw3pTZpEnEYam5quRrGUoDC+CfjA3d3MTqnl8e8CrgfaxLR1dvdFAO6+yMw6he3dgE9itlsQtq0Plyu3b8LMhhGMNJOVlUVeXl4t426d/Pz8zW8kdUb9nTzq6+RRXyeP+jp5atvXS6dM4ecPP6TpNtvQ9eSTk/7veUOm73XdqKlA/iPBlIcHgKfM7NnaHNjMTgCWuvvnZnZkPLtU0eY1tG/a6D4KGAWQk5PjHTp0iC9sHYriPRsz9XfyqK+TR32dPOrr5KlNX38YXvd430svpYtuDFJr+l5vvZpuNf0vdz8QOImgSH0J6GpmfzCzneM49qHASWY2B3gGOMrMxgJLwmkThM9Lw+0XAN1j9s8CFobtWVW0i4iISIpZ/sMPzHzpJdKbNmW/K66IOo40UvFcxWK2u4909z2B/YG2wKQ49rvR3bPcvSfBSPTb7n4eMAEYEm42BHg5XJ4AnG1mzcxse4KT8T4Lp2MUmNlB4dUrBsfsIyIiIilk6h13gDu7DxlCq+22izqONFK1uiOeu38DfEMw/WJL3QKMN7OLgHnAGeGxp5vZeCAXKAEuc/fScJ/fAaOBFgTF+WYLdBEREWlYCpcsYfoTT4AZOdddF3UcacSScstod38XeDdc/gXoW812I4GRVbRPBfZIXEIRERGJ2hf33ktpURE7nXwy7XfZJeo40ojFdR1kERERkUQqXr2aL++/H4D9f//7iNNIY1fTdZDfCp//mbw4IiIi0hh98+ijrFuxgm6HHkq3Qw6JOo40cjVNsehiZr8iuBLFM1S63Jq7T0toMhEREWkUStevZ+qddwIaPZb6oaYC+c8Et4HOAu6stM6BoxIVSkRERBqPH557joJ582i/yy7seOKJUccRqb5AdvfngefN7E/ufnMSM4mIiEgj4e5Mue02AHKGD8fSdHqURG+zV7Fw95vN7CTgiLDpXXd/NbGxREREpDGY99ZbLP3yS1p27kzv886LOo4IEMdVLMzsH8BVBNcnzgWuCttEREREtspnt94KQJ+rriKjefOI04gE4rkO8m+Afdy9DMDMngC+AG5MZDARERFJbUu//JK5b75Jk1at2PuSS6KOI1Ih3ok+28Qst01ADhEREWlkyuce7zV0KM3btYs4jcgG8Ywg/wP4wszeIbjU2xFo9FhERES2Qv7cuXz37LNYejp9rrkm6jgiG4nnJL2nzexdYH+CAvkP7r440cFEREQkdU276y68tJTdBg4kMzs76jgiG4lnBBl3XwRMSHAWERERaQTWrVjB1w8/DOjGIFI/6WKDIiIiklRfPvAA6wsL6XnssXTae++o44hsQgWyiIiIJE3JunVMu+ceAPa//vqI04hUrcYC2czSzOzbZIURERGR1JY7Zgxrliyh0777kn3UUVHHEalSjQVyeO3jr8xMs+dFRERkq3hZGVNuvx0I5h6bWcSJRKoWz0l6XYDpZvYZUFje6O4nJSyViIiIpJxZEyaw4ocfyOzRg13OOCPqOCLViqdA/mvCU4iIiEjKK78xSM6115KWEdeFtEQiEc91kN8zsx5AL3f/r5m1BNITH01ERERSxc8ffsjCjz6iefv27HHRRVHHEanRZq9iYWZDgeeBh8KmbsBLCcwkIiIiKaZ89HifSy+laatWEacRqVk8l3m7DDgUWAXg7jOBTokMJSIiIqlj5cyZzJowgfRmzdj38sujjiOyWfEUyEXuXlz+wswyAE9cJBEREUkFuePGMapnT1465BBwp+uhh9Kqc+eoY4lsVjwF8ntm9keghZkdAzwHvJLYWCIiItKQ5Y4bx+Rhw1g1d25F28KPPiJ33LgIU4nEJ54C+QZgGfANcDEwEbgpkaFERESkYftgxAhK1qzZqK103To+GDEiokQi8YvnKhZlZvYE8CnB1Irv3V1TLERERGQTa5cv5/vx4zcaOY61at68JCcSqb3NFshm9hvgQeBHwIDtzexid5+U6HAiIiJS/5UUFfHTxInkjhnD7Ndeo7S4uNptM7N1c16p/+K5SvcdwK/dfRaAme0IvAaoQBYREWmk3J2FH39M7pgxfD9+POuWLwfA0tLoeeyxtN1hB6Y/8QQla9dW7JPRsiWHjRwZVWSRuMVTIC8tL45Ds4GlCcojIiIi9djKH38kd+xYcseMYeWPP1a0d9x7b3oPGsRu55xD665dAeh22GF8MGIEq+bNIzM7m8NGjqT3wIFRRReJW7UFspmdGi5ON7OJwHiCOchnAFOSkE1ERETqgfJ5xbljxrDwo48q2lt37cqu557L7oMG0XGvvTbZr/fAgfQeOJC8vDw6dOiQzMgiW6WmEeQTY5aXAL8Kl5cB7RKWSERERCIXO6/4x1dfpWz9egCatGpFr1NPpfegQWQfdRRp6ekRJxWpe9UWyO5+QTKDiIiISLQ2mlf87LOsW7EC2DCvuPegQex0yim6VbSkvHiuYrE9cAXQM3Z7dz8pcbFEREQkWVbMmkXu2LHMGDu26nnF555L6y5dIkwoklzxnKT3EvAowd3zyhKaRkRERJJi7S+/bJhX/PHHFe2tu3Zlt4ED6T1oEB333DPChCLRiadAXufu9yQ8iYiIiCRUSVERs197reJ6xRvNKz7tNHYfNIjuv/615hVLoxdPgXy3mf0FmAwUlTe6+7SEpRIREZE64e4s/OijDdcrjp1X3K9fMK/45JM1r1gkRjwF8p7AIOAoNkyx8PC1iIiI1EMrZs4Mrlc8diz5s2dXtHfaZx96DxrErueco3nFItWIp0A+BdjB3au/b6SIiIhEbu0vv/Dds8+SO2YMiz75pKK9dbduG+YV77FHhAlFGoZ4CuSvgG3Q3fNERETqnZKiIma/+mowr3jixA3zilu3ZufTTqP3oEF0P/JIzSsWqYV4CuTOwHdmNoWN5yDrMm8iIiJJkjtuXMVtm9t0787uQ4awZskSvh8/nqKVK4FwXnH//uw+aBA7DhigecUiWyieAvkvCU8hIiIi1codN47Jw4ZRsmYNAAXz5vHJzTdXrO+0zz70HjyY3c45h1bbbRdVTJGUsdkC2d3fS0YQERERqdr//vjHiuI4VtPMTM758EPNKxapY/HcSa+A4KoVAE2BJkChu2cmMpiIiIiAl5VRMG9eleuKCwpUHIskQDwjyG1iX5vZycABiQokIiIigdL163njwgurXZ+ZnZ3ENCKNR1ptd3D3l9A1kEVERBKquLCQ/5x0Erljx5LWtCnpzZpttD6jZUsOGzkyonQiqS2eKRanxrxMA3LYMOVCRERE6tiavDxe/M1vWPzZZ7To0IFTJ05kxQ8/VFzFIjM7m8NGjqT3wIFRRxVJSfFcxeLEmOUSYA4wICFpREREGrlV8+bx/LHHsvz778ns0YPTJ0+m/c4702X//VUQiyRJPHOQL0hGEBERkcYub/p0nu/Xj9U//0yHPffk9Ndfp3XXrlHHEml0qi2QzezPNezn7n5zDetFRESkFn7+8ENePOEEilauJOvwwzl5wgSab7NN1LFEGqWaTtIrrOIBcBHwhwTnEhERaTR+fOUVnjv6aIpWrmSnAQM47Y03VByLRKjaEWR3v6N82czaAFcBFwDPAHdUt5+IiIjE75vHH2fy0KF4aSl7/va3HPPAA6RlxHOKkIgkSo2XeTOz9mb2N+BrgmJ6P3f/g7svTUo6ERGRFOXufPrPf/LGhRfipaUcdNNNHDtqlIpjkXqgpjnItwGnAqOAPd19ddJSiYiIpDAvK+Pd4cP5/F//AjOOuvtu9rviiqhjiUiopl9TrwOKgJuAEWZW3m4EJ+npVtMiIiK1VFpczOsXXMCMp54irUkTjh8zhl3POivqWCISo6Y5yLW+y56IiIhUr3j1aiacfjpz3niDJq1bc/J//kOPo4+OOpaIVKKJTiIiIkmw0d3xOnbktIkT2S4nJ+pYIlIFFcgiIiIJlj93Li/06xfcHa9nT86YPJl2vXpFHUtEqpGwaRRm1t3M3jGzGWY23cyuCtvbm9mbZjYzfG4Xs8+NZjbLzL43s34x7X3M7Jtw3T0WMyFaRESkPlv27bc8fcghLP/+ezrutRfnfvSRimORei6R84xLgOvcfTfgIOAyM+sN3AC85e69gLfC14TrzgZ2B/oD95tZenisB4BhQK/w0T+BuUVEROrEgg8+4JnDD2f1woVkHXEEZ733Hq27dIk6lohsRsIKZHdf5O7TwuUCYAbQDRgAPBFu9gRwcrg8AHjG3Yvc/SdgFnCAmXUBMt39Y3d34MmYfUREROqlH195heePOYailSvpdcopnK6744k0GEmZg2xmPYF9gU+Bzu6+CIIi2sw6hZt1Az6J2W1B2LY+XK7cXtX7DCMYaSYrK4u8vLw6/BSbl5+fn9T3a+zU38mjvk4e9XXyJLKvZ44bx0fXXYeXlrLz4MEcdOutrFy9GlY3zlsK6HudPOrrupHwAtnMWgMvAFe7+6oapg9XtcJraN+00X0UwY1NyMnJ8Q4dOtQ+8FaK4j0bM/V38qivk0d9nTx13dfuzme33MKHf/wjAAf96U8c+te/olNn9L1OJvX11ktogWxmTQiK43Hu/mLYvMTMuoSjx12A8ttWLwC6x+yeBSwM27OqaBcREak3vKyMd669lml33w1m9L33Xva97LKoY4nIFkjkVSwMeBSY4e53xqyaAAwJl4cAL8e0n21mzcxse4KT8T4Lp2MUmNlB4TEHx+wjIiISudLiYiYOGsS0u+8mrUkTTnjmGRXHIg1YIkeQDwUGAd+Y2Zdh2x+BW4DxZnYRMA84A8Ddp5vZeCCX4AoYl7l7abjf74DRQAtgUvgQERGJXPHq1Uw47TTmTJ4c3B3vpZfo0bdv1LFEZCskrEB29w+oev4wQJX/53D3kcDIKtqnAnvUXToREZGtt2bZsuDueFOm0LJTJ06bNInO++0XdSwR2Uq6k56IiMgWyJ8zh+f79WPFDz/QdvvtOX3yZNrttFPUsUSkDqhAFhERqaVl33zD8/36UbhoER333pvTJk3SDUBEUkgi76QnIiKSchb87388c/jhFC5aRNavfsXZujueSMpRgSwiIhKnWS+/zPPHHktRfj69Tj2V019/nWZt20YdS0TqmApkERGROHz9yCO8fOqplKxbx94XX8yJ48eT0bx51LFEJAFUIIuIiNTA3fnk739n8tCheFkZB//5zxz9wAOkpadHHU1EEkQn6YmIiFTDy8p455prmHbPPcHd8f79b/a99NKoY4lIgqlAFhERqUJpcTGThgzhu2eeIb1pU44fN45dTj896lgikgQqkEVERCopLijg5VNPZe5//0vTNm04+aWXyD7qqKhjiUiSqEAWERGJsWbZMl44/niWTJ0a3B3v9dfpvO++UccSkSRSgSwiIhLKnzOH5489lhUzZ9J2hx04/Y03dHc8kUZIBbKIiAiw7Ouveb5/fwoXLaLTPvtw2qRJtNpuu6hjiUgEdJk3ERFp9Oa//z7PHHEEhYsW0f3Xv+as995TcSzSiKlAFhGRRm3mSy9tuDveaadx2sSJNMvMjDqWiERIUyxERKRRyR03jg9GjGDVvHk0b9eOdcuXA7D3JZfQ99//1g1AREQFsoiINB6548YxedgwStasAagojnudeipH338/ZhZlPBGpJzTFQkREGo0PRoyoKI5jLfn8cxXHIlJBBbKIiDQKiz//nFVz51a5btW8eUlOIyL1mQpkERFJWV5WxuyJE3n2qKMYm5NT7XaZ2dlJTCUi9Z3mIIuISMopKSpixrhxTL3jDn7JzQWgaZs2dDv8cOa/8w4la9dWbJvRsiWHjRwZVVQRqYdUIIuISMpYt2IFXz34INPuuYfCxYsBaN2tG/tddRV7DxtGs7ZtN7qKRWZ2NoeNHEnvgQMjTi4i9YkKZBERafDy58zh87vu4ptHHmF9YSEAHffai5zhw9n1rLNIb9q0YtveAwfSe+BA8vLy6NChQ1SRRaQeU4EsIiIN1uKpU5ly++388NxzeFkZAD2OOYb9hw+nxzHH6MoUIrJFVCCLiEiD4mVlzJ40iam33878d98FIC0jg90GDiTnuuvotPfe0QYUkQZPBbKIiDQIJUVFzBg7lil33MHyGTOA4MS7vS6+mP2uvJLM7t0jTigiqUIFsoiI1Gtrly+vOPFuzZIlALTJymK/q69mr9/+lmZt20acUERSjQpkERGpl1b+9BPT7rqLbx59dMOJd3vvzf7Dh7PLWWeR3qRJxAlFJFWpQBYRkXpl0ZQpTL39dn54/vmKE+96HnssOcOH0+Poo3XinYgknApkERGJXPkd76bcfjsL3nsP2HDi3f7Dh9Nxr70iTigijYkKZBERiUzJunXMGDdu4xPvMjPZOzzxrk1WVsQJRaQxUoEsIiJJt3b5cr564AGm3XvvhhPvunenz9VXs+dvf0uzzMyIE4pIY6YCWUREkmbl7NnBHe8efZSSNWuA8MS73/+eXc48UyfeiUi9oAJZREQSbtGUKUy57TZmvvDChhPv+vVj/+HDye7bVyfeiUi9ogJZREQSwsvKmP3aa8GJd++/D0Bakyb0HjSInGuv1Yl3IlJvqUAWEZE6VbJuHbljxzL1jjtY/t13QHji3SWXBCfedesWcUIRkZqpQBYRkS2SO24cH4wYwap588jMzubAG29kzbJlfHHvvaxZuhTQiXci0jCpQBYRkVrLHTeOycOGVZxot2ruXN685JKK9Z322Yf9f/97dj7jDJ14JyINjgpkERGJm7uzau5c3rn66oriOFZ68+ac+uqrZB91lE68E5EGSwWyiIhUq7S4mCXTprHwo4/4+aOPWPjRRxQuWlT99kVF9OjbN4kJRUTqngpkERGpULh0KYs+/riiGF48ZQqlRUUbbdO8fXtK1q6lZO3aTfbPzM5OVlQRkYRRgSwi0kh5WRl5ubksDIvhnz/8kJWzZm2yXfvddqPbIYfQNXy033lnZjz99EZzkAEyWrbksJEjk/kRREQSQgWyiEgjUVxQwKJPP60YHV70yScU5edvtE1Gy5Z0OeAAuh16KF0POYQuBx1Ei/btNzlW74EDATa6isVhI0dWtIuINGQqkEVEUpC7kz9nTsXo8MKPPmLZ119X3MWuXJvs7I1GhzvutVfcV53oPXCgCmIRSUkqkEVEUkBJURFLv/iiYqrEwo8+onDx4o22ScvIoHOfPnQ95JBghPjgg2mTlRVRYhGR+ksFsohIA1S4dOlGo8OLp07d5GS6FttuWzEy3PWQQ9guJ4cmLVtGlFhEpOFQgSwiUg9Uvitd7HzestJSfglPpiufP1zVyXTb9u5dUQx3O+QQ2u28s65FLCKyBVQgi4hErKq70r1x0UXMfPFF1q9ezcJPPqF41aqN9mnSqhVdDjxwwwjxQQfRvF27KOKLiKQcFcgiIhFYv2YNBfPnUzB/Pm9fddUmd6UrLSpi5osvVrzO7NFjo9HhjnvtRVqG/hcuIpII+r+riEgdKy0upmDBgooCuGD+fFbFLBfMn8+65cvjOtaJzz0XnEzXrVuCU4uISDkVyCIitVBWWkrhokVVFr3lj8IlS8C9xuOkN21K66ws2nTvzuKpUykpLNxkm8wePdjl9NMT9VFERKQaKpBFRELuzpplyzYe+Z03b6PXqxcuxEtLazyOpaVVFL/lj8yY5Tbdu9OyY0csLQ3YdA4y6K50IiJRUoEsIimluqtBuDtFK1fWOPJbsGDBJpdKq0rLzp2rLHrLH627dKnV/GDdlU5EpH5RgSwiDVJpcTFF+fkUr1pFUX4+RatW8eOECXxx332UFRcDwdUgJg0ezHvXX09xfj7rq5jGUFnzdu02HvnNzt64+O3WjYxmzer885TflS4vL48OHTrU+fFFRCR+KpBFpFo1XZt3S3lZGcUFBRVFbXGl59iit/Jz7HI8I73l71e4cCEATVq3rnHkt0337jRt1WqrPp+IiDR8KpBFkiARhWaiVXVt3slDh1KUn0+Po4+utnDd7HNBQZ3kS8vIoFnbtjTNzKx4XvD++1VvbMbly5fTrG1b3ThDREQ2SwVyI9YQizZoeLmrLDSHDQOIO7e7U1ZSQmlREaVFRZSsW1fl8uZelxQVURq+LinfZt26jZbL1y394gvK1q/fKEfJ2rW8ddllW90nTdu02aS4rem5WWYmTdu23Wg5o3nzTYrdUT17smru3E3eLzM7m+bbbLPVuUVEpHFoMAWymfUH7gbSgUfc/ZaII1VoaAUb1E3RFoWacu927rmUlZTgpaUbPdd2eUv3KystxcO22OUvH3hgk5tAlKxZw+ShQ5nx1FObFqnVFLmbu2xYMrXr1Sv+orZycdumTcXVG+raYSNH6moQIiKy1czr0T+61TGzdOAH4BhgATAFOMfdc6vbJycnx6dOnZrwbFVdnimtSRN6nXoqnfbdd0NR44671/gcbBYux7ldTdvXtN2Mp55i/erVm3yejFat6HXyyXhZGV5WFmwfLsc+qmpPxrZr8/KCtkbI0tNJb9aMjObNSW/WbNPlZs1Ir+b1Jsvh6yqXw+O+dMopFC5atEmOzB49GDZnTvI7IE4N8RfWWDpJL3nU18mjvk4e9XXtmNnn7p6zSXsDKZAPBv7P3fuFr28EcPd/VLdPsgrk6v6kK9Gw9HTSMjIqnuNaTk/HwrbY5dpsW9PyZ7feStHKlZtkbdGhA/0ff3yTQre6IjgtPT2pfVndtXmPHTWqQRWcDY3+cUse9XXyqK+TR31dO9UVyA1likU3YH7M6wXAgZU3MrNhwDCArKws8vLyEh5s1bx51a7b4/LLIWaOpJmBWcVzlcvBhpsuV94+5njVtcceo/Jxpo0cSXEVRVuzdu04YOTI4E/g4T6WlgZpaRvawmUzq2ivvFyxT2x7+euYY8Suq+r9KvYP21855hjWhFckiNUqK4vTp02rnydgtWvHR9deS+natRVN6S1akHPzzbQ96KBNNndgffigrAzWrAkeSdapXz8OvuMOpo0cSeHPP9OqWzf2GzGCTv36JeW/rcYqPz8/6giNhvo6edTXyaO+rhsNpUCuqurZZOjb3UcBoyAYQU7Gb1CZ2dlVnxTUowf977034e+/pdp36VLl6GDfe++t16ODR956a5W5f3XLLXTs2DHCZNXrcMkltGnTpkH+2b/DJZdw4CWXaEQiydTXyaO+Th71dfKor7deQymQFwDdY15nAZsOI0agoZ4U1FDv3NWQc9f3jCIiIhJoKAXyFKCXmW0P/AycDZwbbaRAQy3YoOEWbbrjmIiIiCRSgyiQ3b3EzC4H3iC4zNtj7j494lgVVLCJiIiIpI4GUSADuPtEYGLUOUREREQktSXmav0iIiIiIg2UCmQRERERkRgqkEVEREREYqhAFhERERGJoQJZRERERCSGCmQRERERkRgqkEVEREREYpi7R50hIcxsGTA3yW/bAchL8ns2Zurv5FFfJ4/6OnnU18mjvk4e9XXt9HD3jpUbU7ZAjoKZTXX3nKhzNBbq7+RRXyeP+jp51NfJo75OHvV13dAUCxERERGRGCqQRURERERiqECuW6OiDtDIqL+TR32dPOrr5FFfJ4/6OnnU13VAc5BFRERERGJoBFlEREREJIYKZBERERGRGCqQ64iZ9Tez781slpndEHWeVGVm3c3sHTObYWbTzeyqqDOlOjNLN7MvzOzVqLOkMjPbxsyeN7Pvwu/3wVFnSlVmdk34/49vzexpM2sedaZUYmaPmdlSM/s2pq29mb1pZjPD53ZRZkwV1fT1beH/R742s/+Y2TYRRmywVCDXATNLB+4DjgN6A+eYWe9oU6WsEuA6d98NOAi4TH2dcFcBM6IO0QjcDbzu7rsCe6M+Twgz6wZcCeS4+x5AOnB2tKlSzmigf6W2G4C33L0X8Fb4WrbeaDbt6zeBPdx9L+AH4MZkh0oFKpDrxgHALHef7e7FwDPAgIgzpSR3X+Tu08LlAoIiolu0qVKXmWUBvwEeiTpLKjOzTOAI4FEAdy9295WRhkptGUALM8sAWgILI86TUtz9fWB5peYBwBPh8hPAycnMlKqq6mt3n+zuJeHLT4CspAdLASqQ60Y3YH7M6wWoaEs4M+sJ7At8GnGUVHYXcD1QFnGOVLcDsAx4PJzO8oiZtYo6VCpy95+B24F5wCIg390nR5uqUejs7osgGOgAOkWcp7G4EJgUdYiGSAVy3bAq2nT9vAQys9bAC8DV7r4q6jypyMxOAJa6++dRZ2kEMoD9gAfcfV+gEP0JOiHCua8DgO2BrkArMzsv2lQidc/MRhBMSxwXdZaGSAVy3VgAdI95nYX+ZJcwZtaEoDge5+4vRp0nhR0KnGRmcwimDR1lZmOjjZSyFgAL3L38ryHPExTMUveOBn5y92Xuvh54ETgk4kyNwRIz6wIQPi+NOE9KM7MhwAnAQNcNL7aICuS6MQXoZWbbm1lTghM+JkScKSWZmRHM05zh7ndGnSeVufuN7p7l7j0JvtNvu7tG2hLA3RcD881sl7CpL5AbYaRUNg84yMxahv8/6YtOiEyGCcCQcHkI8HKEWVKamfUH/gCc5O5ros7TUKlArgPhZPjLgTcI/kc73t2nR5sqZR0KDCIYzfwyfBwfdSiROnAFMM7Mvgb2Af4ebZzUFI7SPw9MA74h+HdQt+atQ2b2NPAxsIuZLTCzi4BbgGPMbCZwTPhatlI1ff1voA3wZvhv5IORhmygdKtpEREREZEYGkEWEREREYmhAllEREREJIYKZBERERGRGCqQRURERERiqEAWEREREYmhAllEpAEysxFmNt3Mvg4v5XSgmV1tZi2jziYi0tDpMm8iIg2MmR0M3Akc6e5FZtYBaAp8BOS4e16kAUVEGjiNIIuINDxdgDx3LwIIC+LTga7AO2b2DoCZPWBmU8OR5r+W72xmx5vZd2b2gZndY2avhu2tzOwxM5tiZl+Y2YDkfzQRkehpBFlEpIExs9bAB0BL4L/As+7+npnNIWYE2czau/tyM0sH3gKuBH4AZgJHuPtP4Z242rj7CWb2dyDX3cea2TbAZ8C+7l6Y7M8oIhIljSCLiDQw7r4a6AMMA5YBz5rZ+VVseqaZTQO+AHYHegO7ArPd/adwm6djtj8WuMHMvgTeBZoD2Qn4CCIi9VpG1AFERKT23L2UoIh918y+AYbErjez7YHhwP7uvsLMRhMUvFbDYQ04zd2/T0hoEZEGQiPIIiINjJntYma9Ypr2AeYCBUCbsC0TKATyzawzcFzY/h2wg5n1DF+fFXOcN4ArzMzC99k3IR9ARKSe0wiyiEjD0xq4N5wnXALMIphucQ4wycwWufuvzewLYDowG/gQwN3XmtmlwOtmlkcwz7jczcBdwNdhkTwHOCEpn0hEpB7RSXoiIo2MmbV299VhEXwfMNPd/xV1LhGR+kJTLEREGp+h4Yl404G2wEPRxhERqV80giwiIiIiEkMjyCIiIiIiMVQgi4iIiIjEUIEsIiIiIhJDBbKIiIiISAwVyCIiIiIiMf4/pjmBSqTI98UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x864 with 14 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "✅ All visualization completed.\n",
      "   Check folder 'gmt_visualization/' for detailed images.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from typing import List, Set, Tuple\n",
    "import os\n",
    "\n",
    "# ----------------------------\n",
    "# 1. 生成极度稀疏信号（雷达脉冲）\n",
    "# ----------------------------\n",
    "def generate_sparse_signal(N=8192, num_pulses=5):\n",
    "    \"\"\"生成 N 点信号，仅 num_pulses 个非零点\"\"\"\n",
    "    x = np.zeros(N, dtype=complex)\n",
    "    indices = np.random.choice(N, num_pulses, replace=False)\n",
    "    x[indices] = np.random.randn(num_pulses) + 1j * np.random.randn(num_pulses)\n",
    "    return x, indices\n",
    "\n",
    "# ----------------------------\n",
    "# 2. GMT-FFT with full trace (白盒化版本)\n",
    "# ----------------------------\n",
    "def gmt_fft_full_trace(x: np.ndarray, eps=1e-5) -> Tuple[\n",
    "    np.ndarray,                    # 最终频域结果\n",
    "    List[Set[int]],               # 每层活跃节点集合\n",
    "    List[np.ndarray],             # 每层变换前的信号值\n",
    "    List[np.ndarray]              # 每层蝴蝶连接图（稀疏矩阵表示）\n",
    "]:\n",
    "    x = x.copy()\n",
    "    N = len(x)\n",
    "    num_bits = N.bit_length() - 1\n",
    "\n",
    "    # 位反转索引\n",
    "    rev_indices = [sum(((n >> i) & 1) << (num_bits - 1 - i) for i in range(num_bits)) for n in range(N)]\n",
    "    x = x[rev_indices]\n",
    "\n",
    "    # 存储每层状态\n",
    "    active_sets = []           # 活跃节点集合\n",
    "    signal_states = []         # 每层输入信号\n",
    "    butterfly_graphs = []      # 每层的蝴蝶连接（用稀疏邻接矩阵表示）\n",
    "\n",
    "    # 初始状态\n",
    "    active = set(np.nonzero(np.abs(x) > eps)[0])\n",
    "    active_sets.append(active.copy())\n",
    "    signal_states.append(x.copy())\n",
    "\n",
    "    # 记录初始非零位置\n",
    "    print(f\"Initial non-zero indices (bit-reversed): {sorted(active)}\")\n",
    "\n",
    "    # 迭代每一级\n",
    "    for s in range(1, num_bits + 1):\n",
    "        m = 1 << s\n",
    "        w_m = np.exp(-2j * np.pi / m)\n",
    "        next_active = set()\n",
    "        graph = np.zeros((N, N))  # 稀疏连接图\n",
    "\n",
    "        for k in range(0, N, m):\n",
    "            block_active = any(idx in active for idx in range(k, k + m))\n",
    "            if not block_active:\n",
    "                continue\n",
    "\n",
    "            w = 1.0\n",
    "            for j in range(m // 2):\n",
    "                idx1 = k + j\n",
    "                idx2 = k + j + m // 2\n",
    "                if idx1 in active or idx2 in active:\n",
    "                    # 记录蝴蝶连接\n",
    "                    graph[idx1, idx1] = 1\n",
    "                    graph[idx1, idx2] = 1\n",
    "                    graph[idx2, idx1] = 1\n",
    "                    graph[idx2, idx2] = 1\n",
    "                    # 执行变换\n",
    "                    t = w * x[idx2]\n",
    "                    u = x[idx1]\n",
    "                    x[idx1] = u + t\n",
    "                    x[idx2] = u - t\n",
    "                    next_active.add(idx1)\n",
    "                    next_active.add(idx2)\n",
    "                w *= w_m\n",
    "\n",
    "        active = next_active\n",
    "        active_sets.append(active.copy())\n",
    "        signal_states.append(x.copy())\n",
    "        butterfly_graphs.append(graph)\n",
    "\n",
    "    return x, active_sets, signal_states, butterfly_graphs\n",
    "\n",
    "# ----------------------------\n",
    "# 3. 可视化函数\n",
    "# ----------------------------\n",
    "def visualize_gmt_fft_process(active_sets, signal_states, butterfly_graphs, N):\n",
    "    num_stages = len(active_sets)\n",
    "    stages = list(range(num_stages))\n",
    "\n",
    "    os.makedirs(\"gmt_visualization\", exist_ok=True)\n",
    "\n",
    "    # ===================================================\n",
    "    # 图 1: 活跃节点演化热力图（纵向：stage，横向：index）\n",
    "    # ===================================================\n",
    "    plt.figure(figsize=(14, 6))\n",
    "    heatmap = np.zeros((num_stages, N))\n",
    "    for stage, active in enumerate(active_sets):\n",
    "        for idx in active:\n",
    "            heatmap[stage, idx] = 1\n",
    "\n",
    "    plt.imshow(heatmap, aspect='auto', cmap='Reds', interpolation='none')\n",
    "    plt.xlabel('Index (Bit-Reversed Order)')\n",
    "    plt.ylabel('Stage')\n",
    "    plt.title('Active Node Propagation in GMT-FFT\\n(Red = Computed Path)')\n",
    "    plt.colorbar(label='Active')\n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('gmt_visualization/active_propagation.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "    # ===================================================\n",
    "    # 图 2: 活跃节点数量变化曲线\n",
    "    # ===================================================\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    sizes = [len(active) for active in active_sets]\n",
    "    plt.plot(stages, sizes, 'o-', color='darkred', linewidth=2, markersize=6)\n",
    "    plt.xlabel('Stage')\n",
    "    plt.ylabel('Number of Active Nodes')\n",
    "    plt.title('Evolution of Active Node Count Across Stages')\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('gmt_visualization/active_count_evolution.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "    # ===================================================\n",
    "    # 图 3: 每层信号幅值分布（多子图）\n",
    "    # ===================================================\n",
    "    cols = 4\n",
    "    rows = (num_stages + cols - 1) // cols\n",
    "    plt.figure(figsize=(16, rows * 3))\n",
    "\n",
    "    for stage in range(num_stages):\n",
    "        plt.subplot(rows, cols, stage + 1)\n",
    "        mag = np.abs(signal_states[stage])\n",
    "        plt.plot(mag, color='steelblue', linewidth=0.8)\n",
    "        plt.axhline(y=1e-5, color='r', linestyle='--', linewidth=1, label='Threshold')\n",
    "        plt.yscale('log')\n",
    "        plt.ylim(1e-6, max(mag.max(), 1e-4))\n",
    "        plt.title(f'Stage {stage}: Signal Magnitude')\n",
    "        plt.xlabel('Index')\n",
    "        plt.ylabel('|x|')\n",
    "        plt.legend()\n",
    "        plt.grid(True, alpha=0.3)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('gmt_visualization/signal_magnitude_per_stage.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "   \n",
    "\n",
    "    # ===================================================\n",
    "    # 图 5: 活跃路径三维演化图（可选）\n",
    "    # ===================================================\n",
    "    from mpl_toolkits.mplot3d import Axes3D\n",
    "    fig = plt.figure(figsize=(12, 8))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "    for stage, active in enumerate(active_sets):\n",
    "        for idx in active:\n",
    "            ax.scatter(stage, idx, np.abs(signal_states[stage][idx]), \n",
    "                      c='red', s=6, alpha=0.8)\n",
    "\n",
    "    ax.set_xlabel('Stage')\n",
    "    ax.set_ylabel('Index')\n",
    "    ax.set_zlabel('|Value|')\n",
    "    ax.set_title('3D Evolution of Active Paths in GMT-FFT')\n",
    "    plt.tight_layout()\n",
    "    #plt.savefig('gmt_visualization/3d_active_evolution.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "\n",
    "    \n",
    "\n",
    "# ----------------------------\n",
    "# 4. 主函数：只做可视化\n",
    "# ----------------------------\n",
    "def main():\n",
    "    N = 8192\n",
    "    x, true_indices = generate_sparse_signal(N, num_pulses=5)\n",
    "    print(f\"Original non-zero indices: {sorted(true_indices)}\")\n",
    "\n",
    "    # 执行带完整追踪的 GMT-FFT\n",
    "    _, active_sets, signal_states, butterfly_graphs = gmt_fft_full_trace(x, eps=1e-5)\n",
    "\n",
    "    # 可视化所有过程\n",
    "    visualize_gmt_fft_process(active_sets, signal_states, butterfly_graphs, N)\n",
    "\n",
    "    print(\"\\n✅ All visualization completed.\")\n",
    "    print(\"   Check folder 'gmt_visualization/' for detailed images.\")\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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